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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Equations/158839: Hi I am a granfather of 75 yrs old. trying to help out his grandaughter. she has been working on a algebra problem for hours finish all but one question. Sent her home with her mother who tried also.she was so tired I sent her to bed. Its been 60 yrs since I had to do math..lol She just doesn't understand how to begin..Honestly we tried. if you can help it would be wonderful. the question is two trains traveling in different directions one at 55mph and the other at 45mph they traveled a total of 400 miles how long did it take to go that distance... she doesn't know how to work out the formula...rate and time. thank you1 solutions Answer 116981 by stanbon(57282)   on 2008-09-24 23:29:38 (Show Source): You can put this solution on YOUR website!two trains traveling in different directions one at 55mph and the other at 45mph they traveled a total of 400 miles how long did it take to go that distance... ----------------------- The basic formula is: distance = rate * time ------------------------- 1st train DATA: rate = 55 mph ; distance = x miles ; time = d/r = x/55 hrs. --------------------- 2nd train DATA: rate = 45 mph ; distance = (400-x) miles ; time = d/r = (400-x)/45 hrs ------------------------ EQUATION: time = time x/55 = (400-x)/45 Cross-multiply to get: 45x = 55(400-x) 45x = 55*400 - 55x 100x = 55*400 x = 55*4 x = 220 miles ---------------- time = distance/rate time = 220 / 55 = 4 hours The time is the same for both of the trains. ================== Another way to do the problem. The trains are going away from one another at (45+55) = 100 mph The time for them to be 400 miles apart is 400/100 = 4 hours. ======================= Cheers, Stan H.
 Polynomials-and-rational-expressions/158728: when is the LCM of two polynomials eqaul to their product? given the expression 1/(x-5). Is it possible to choose a value for x for which the value of the expression is greater than 10?1 solutions Answer 116924 by stanbon(57282)   on 2008-09-24 15:52:40 (Show Source): You can put this solution on YOUR website!When is the LCM of two polynomials equal to their product? When the denominators are inverse of one another and the product of the numerators is "1". --------------------------- given the expression 1/(x-5). Is it possible to choose a value for x for which the value of the expression is greater than 10? INEQUALITY: 1/(x-5) > 10 ----- x cannot be 5: Draw a number line and mark x=5 ------------ Let x be greater than 5; then x-5 is positive. Multiply both sides of the inequality by x-5 to get: 1 > 10x - 50 10x < 51 x < 5.1 ------ Solutions: 5 < x < 5.1 ------------- Cheers, Stan H.
 Functions/158744: Fill in the missing values in the function table: Input(x) Output (y) x=1 y=8 x=2 y=14 x=3 y=Unknown value x=Unknown value y=24 x=Unknown value y=28 x=6 y=Unknown value Please help me. I am stumped!1 solutions Answer 116922 by stanbon(57282)   on 2008-09-24 15:14:38 (Show Source): You can put this solution on YOUR website!Fill in the missing values in the function table: Input(x) Output (y) x=1 y=8 x=2 y=14 x=3 y=Unknown value x=Unknown value y=24 x=Unknown value y=28 x=6 y=Unknown value ---------------------- Using the 1st two lines you have (1,8) and (2,14) slope = (14-8)/(2-1) = 6 intercept: 8 = 6*1 + b b = 2 -------- EQUATION: y = 6x + 2 --------------- Using that equation you can fill in the missing values. ========================== Cheers, Stan H.
 Polynomials-and-rational-expressions/158746: can someone help me with this question; If a function has an odd degree and a negative leading coefficient, then what is the minimum number of zeroes it must possess/ 1. 1 2. 0 3. -1 4. This cannot be determined based on the given information.1 solutions Answer 116921 by stanbon(57282)   on 2008-09-24 15:09:40 (Show Source): You can put this solution on YOUR website!If a function has an odd degree and a negative leading coefficient, then what is the minimum number of zeroes it must possess/ ------------------------------ Try it with y = x^3 Notice that y is negative if x=-10 Notice that y is positive if x = +10. Somewhere between x = -10 and x= +10 the y-value must have passed thru zero. ----------- Answer: minimum number is one. Cheers, Stan H.
 Polynomials-and-rational-expressions/158747: can someone help me with this question; What is the relationship between the degree of a polynomial and the maximum number of zeroes it can have? 1. The number of zeroes is one less than the degree of the polynomial. 2. The degree of the polynomial is one less than the number of zeroes. 3. They are the same value. 4. The number of zeroes is the square of the degree of the polynomial.1 solutions Answer 116920 by stanbon(57282)   on 2008-09-24 15:03:43 (Show Source): You can put this solution on YOUR website!If you allow Complex Number solutions, the answer is #3. Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/158748: A boat is on sale for \$7995. Find its regular price if it has been marked down \$1350. Find the percent mark down on its orignal price.1 solutions Answer 116919 by stanbon(57282)   on 2008-09-24 15:01:41 (Show Source): You can put this solution on YOUR website!A boat is on sale for \$7995. Find its regular price if it has been marked down \$1350. Find the percent mark down on its orignal price. ------------------------ Let the original price be the percent of mark down: EQUATION: 7995x = 1350 x = 1350/7995 x = 16.9% ============ Cheers, Stan H.
 Polynomials-and-rational-expressions/158749: can someone help me answer this question; If f(x) is a parabola, then: 1. it is a step function 2. it is a continuous, smooth function 3. it is a piecewise function 4. it is a square root function1 solutions Answer 116918 by stanbon(57282)   on 2008-09-24 14:52:59 (Show Source): You can put this solution on YOUR website!Draw a parabola and you will see that #2 is the best answer. Cheers, Stan H.
 Polynomials-and-rational-expressions/158745: A rectangle is three times as long as it is wide. if its length and width is decreased by 2cm its area is decreased by 36 cm^2. Find its original dimensions.1 solutions Answer 116917 by stanbon(57282)   on 2008-09-24 14:51:28 (Show Source): You can put this solution on YOUR website!A rectangle is three times as long as it is wide. if its length and width is decreased by 2cm its area is decreased by 36 cm^2. Find its original dimensions. --------------------------- Original Dimensions: width = x ; length = 3x ----------------------- New Dimensions: width = x-2 ; length = 3x-2 ----------------------- EQUATION: original area - new area = 36 cm^2 3x^2 - (x-2)(3x-2) = 36 3x^2 - [3x^2 - 7x + 4] = 36 7x -4 = 36 7x = 40 x = (40/7) cm (original width) 3x = (120/7) cm(original length) -------------------- Cheers, Stan H.
 Expressions-with-variables/158740: Please help me solve this equation for v if possible: S=(-1/2)gtSquared+vt1 solutions Answer 116913 by stanbon(57282)   on 2008-09-24 13:45:56 (Show Source): You can put this solution on YOUR website!solve this equation for v if possible: S=(-1/2)gtSquared+vt ---------------------------------- Multiply thru by 2 to get: 2S = -gt^2 + 2vt ------------ [2S + gt^2] = 2vt ----------- v = [2S + gt^2]/[2t] ====================== Cheers, Stan H.
 Equations/158742: This question is from textbook Elementary Algebra Solve for b: A= 1/2(a+b)h I know the answer but I just can't figure out how to get b on the one side. Thank you!!!1 solutions Answer 116911 by stanbon(57282)   on 2008-09-24 13:37:53 (Show Source): You can put this solution on YOUR website!A= 1/2(a+b)h --------- 2A = (a+b)h [2A/h] = a+b b = [2A/h] - a =================== Cheers, Stan H.
 Permutations/158731: Suppose you have six families consisting of a mother, a father, and a child. How many ways can the families sit in a row of 18 chairs such that members of each family are sitting together?1 solutions Answer 116910 by stanbon(57282)   on 2008-09-24 13:34:19 (Show Source): You can put this solution on YOUR website!How many ways can the families sit in a row of 18 chairs such that members of each family are sitting together? ---------------------------- # of ways to arrange the families: 6! = 720 # of ways to arrange the members within each family 3! = 6 -------------- Total # of arrangements: 720*6 = 4320 ------------------------------------ Cheers, Stan H.
 Money_Word_Problems/158736: 2. Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the costs for such a station are \$2,500 for setup costs and \$3.00 to administer each test. a. Write an expression that gives the total cost to test x animals. b. You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal. c. Find the average cost per animal for 10 animals. 100 animals. 1,000 animals. d. As the number of animals tested increases, what happens to the average cost to test the animals? Would the average cost ever fall below \$3.00? If so, identify a value that supports your answer. If not, explain how you know. e. How many animals should be tested for the average cost to be \$5.00 per animal? 1 solutions Answer 116908 by stanbon(57282)   on 2008-09-24 13:23:32 (Show Source): You can put this solution on YOUR website!Suppose that the costs for such a station are \$2,500 for setup costs and \$3.00 to administer each test. a. Write an expression that gives the total cost to test x animals. C(x) = 2500 + 3x dollars ------------------------------------ b. You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal. [C(x)]/x = [2500 + 3x]/x ------------------------------- c. Find the average cost per animal for 10 animals. 100 animals. 1,000 animals. For 10 animals: [C(10)] = [2500 + 3*10]/10 = 2800/10 = 280 dollars --- You can do the work for x=100 and for x=1000 ------------------------------- d. As the number of animals tested increases, what happens to the average cost to test the animals? Would the average cost ever fall below \$3.00? If so, identify a value that supports your answer. If not, explain how you know. The horizontal asymptote is 3x/x = 3 The average would not drop below \$3 -------------------------------- e. How many animals should be tested for the average cost to be \$5.00 per animal? Let C(x)=\$5 and solve for "x": 5 = [2500+3x]/x 2x = 2500 x = 1250 animals. ==================== Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/158739: find three consecutive even integers if their sum, decreased by the thrid, equals -221 solutions Answer 116907 by stanbon(57282)   on 2008-09-24 13:10:23 (Show Source): You can put this solution on YOUR website!find three consecutive even integers if their sum, decreased by the thrid, equals -22 ------------------ 1st: 2x 2nd: 2x+2 3rd: 2x+4 -------------- EQUATION: When you say "decreased by the third" do you mean decreased by the third of the consecutive even integers, or do you mean decreased by a third of the sum? ------------------------ Cheers, Stan H.
 Polynomials-and-rational-expressions/158687: 4X^3-XY^21 solutions Answer 116869 by stanbon(57282)   on 2008-09-23 23:54:22 (Show Source): You can put this solution on YOUR website!4X^3-XY^2 = X(4X^2-Y^2) = X(2X-Y)(2X+Y) ==================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/158683: page 43 Chap.7.3 You have \$160 and save \$7 per week. Your friend has \$210 and saves \$5 per week. After how many weeks will each of you have saved the same amount of money?1 solutions Answer 116868 by stanbon(57282)   on 2008-09-23 23:51:15 (Show Source): You can put this solution on YOUR website!You have \$160 and save \$7 per week. Your friend has \$210 and saves \$5 per week. After how many weeks will each of you have saved the same amount of money? ------------------------ EQUATION: 150+7x = 210+5x 2x = 60 x = 30 weeks ---------------- Cheers, Stan H.
 logarithm/158685: 5^x=12 use log to solve for x.1 solutions Answer 116867 by stanbon(57282)   on 2008-09-23 23:43:04 (Show Source): You can put this solution on YOUR website!5^x=12 use log to solve for x. ----------- Take the log of both sides to get: x(log5) = log12 x = [log12] / [log5] ------------ I don't have a calculator with me so maybe you do and can perform the division to solve for "x". ------------------ Cheers, Stan H.
 Equations/158682: This question is from textbook Prealgebra -5w+2+6w=-4+9 This is what I got; I know I need to find the like terms, which are -5w & 6w. -5w + 6w = 1w + 2 = 5 I know I need to balance each side out equally...but not sure how to do that. I'm stuck! Also, not sure how to check my work. This problem is in my text book: Prealgebra Third Edition by Lial Hestwood page 115 #39. Thank you for your help! Pauline1 solutions Answer 116866 by stanbon(57282)   on 2008-09-23 23:38:03 (Show Source): You can put this solution on YOUR website!-5w+2+6w=-4+9 Simplify the left side and the right side of the equation: w + 2 = 5 Subtract 2 from both sides to get: w = 3 ============ Checking; substitute 3 in place of "x" in the original equation: -5*3 + 2 + 6*3 = -4+9 -15 + 2 + 18 = 5 5 = 5 ============== Cheers, Stan H.
 Polynomials-and-rational-expressions/158540: I need help with this multiplication: 3x over 2y * y^2 over 6 = ? Thank you for your help.1 solutions Answer 116800 by stanbon(57282)   on 2008-09-23 08:21:39 (Show Source): You can put this solution on YOUR website!3x over 2y * y^2 over 6 = ? --------------------------------- (3x/2y)* (y^2/6) -------- Cancel any factors that are common to a numerator and a denominator, such as y, and 3, to get: =(x/2)* (y/2) Now multiply the numerators and multiply the denominators to get: =(xy)/4 --------- Cheers, Stan H.
 Functions/158479: Find the domain of the following: 1.f(x)=4.5e 2. g(x)=2^x Show your work and explain how you obtained your answer 3. h(x)=-e^x Description of transformation Equation(s) for the Horizontal Asymptote(s). y-intercept in (x,y) form:1 solutions Answer 116787 by stanbon(57282)   on 2008-09-22 23:52:30 (Show Source): You can put this solution on YOUR website!Find the domain of the following: 1.f(x)=4.5e Domain: all Real Numbers Description: horizontal line thru all points where y = 4.5*2 Horizontal Asymptote: none y-intercept: Let x = 0, then y = 4.5e intercept is (0,4.5e) ------------------------------ 2. g(x)=2^x Show your work and explain how you obtained your answer Domain: all Real Numbers Description: increasing exponential function Horizontal Asymptote: y = 0 y-intercept: Let x=0, then y = 1 Intercept is (0,1) ------------------------------ 3. h(x)=-e^x Domain: all Real Numbers Description: decreasing exponential function Horizontal Asymptote: y = 0 y-intercept: Let x = 0, then y = -1 Intercept is (0,-1) =================================== Cheers, Stan H.
 Exponents/158496: This question is from textbook Math Connections I'm Having A Hard Time Trying To Get This Question Answered. "Can each of the following be expressed as a power of two? If Yes, do so. If No, Explain why not." Problem A: 2^3 * 2^85 I Don't Know What The Questions Means/Wants.1 solutions Answer 116786 by stanbon(57282)   on 2008-09-22 23:35:16 (Show Source): You can put this solution on YOUR website!"Can each of the following be expressed as a power of two? If Yes, do so. If No, Explain why not." Problem A: 2^3 * 2^85 = 2^(3+85) = 2^88 ============= Cheers, Stan H.
 Expressions-with-variables/158514: Define a variable, write an inequality for: Four more than the quotient of a number and 3 is at least that number. I'm stuck about showing the quotient. I wrote 4 + 1/x + 3 > x Please help and thanks, Justin1 solutions Answer 116785 by stanbon(57282)   on 2008-09-22 23:32:26 (Show Source): You can put this solution on YOUR website!Define a variable, write an inequality for: Four more than the quotient of a number and 3 is at least that number. ---------------- Let the number be "x". INEQUALITY: (x/3) + 4 >= x ===================== Cheers, Stan H.
 expressions/158526: This question is from textbook Algerbra 1 Placing planks at equel length end to end, jewels found that three planks where one foot short of the portch length, while four planks were two feet to long. How long was each plank?1 solutions Answer 116784 by stanbon(57282)   on 2008-09-22 23:21:48 (Show Source): You can put this solution on YOUR website!Placing planks at equal length end to end, jewels found that three planks where one foot short of the porch length, while four planks were two feet to long. How long was each plank? ------------------- EQUATION: porch length = porch length 3p+1 = 4p-2 p = 3 ft. Cheers, Stan H.
 Word_Problems_With_Coins/158293: Susan has saved \$85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have. I have tried this a zillion times using 2 separate equations and the elimination method a variety of ways, but cannot seem to get an answer that fits back. If someone can show me the proper equation to be using please then I can solve from there. Thanks. 1 solutions Answer 116670 by stanbon(57282)   on 2008-09-21 23:49:38 (Show Source): You can put this solution on YOUR website!Susan has saved \$85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have. ------------------------ I believe a "looney" is one dollar. If that is right you get the following equations: Value Equation: 25Q + 100L = 8575 Quantity Equation: Q = (3/4)L + 1 ----------------------------------- Rearrange the equations: 4Q - 3L = 4 25Q + 100L = 8575 ------------------------ Multiply the 1st equation by 25; Multiply the 2nd equation by 4. 100Q - 75L = 100 100Q + 400L = 4*8575 ---------------------- Subtract the 1st equation from the 2nd to get: 475L = 4*8575 - 100 ------------------------ I don't have a calculator with me so I'll leave solving "L" to you. When you get "L" substitute into one of the early equation to solve for Q. -------------------------- Cheers, Stan H.
 Travel_Word_Problems/158306: Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way. (i'm in 8th grade, and it just doesn't make sense to me) But I think this is what I am supposed to do, but I don't understand why it works.. if it does. 1 solutions Answer 116669 by stanbon(57282)   on 2008-09-21 23:39:29 (Show Source): You can put this solution on YOUR website!Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way. ------------------------------------- School to home DATA: rate = 20 mph ; distance = x miles ; time = d/r = x/20 hrs --------------------------- home to school DATA: rate = 30 mph ; distance = x miles ; time = d/r = x/30 hrs ----------------------------- EQUATION: time + time = 1.5 hours x/20 + x/30 = 3/2 Multiply thru by 60 to get: 3x + 2x = 90 5x = 90 x = 18 miles (distance each way) ----------- time to drive from home to school = 18/20 = 9/10 hr = 54 minutes time to drive from school to home = 18/30 = 3/5 hr = 36 minutes ====================== Cheers, Stan H.
 Square-cubic-other-roots/158307: How do you solve...?... (x+4)exponent5=-1 ...??? ...Thanks1 solutions Answer 116667 by stanbon(57282)   on 2008-09-21 23:31:38 (Show Source): You can put this solution on YOUR website!(x+4)exponent5=-1 ------------ Take the 5th root of each side to get: x+4 = -1 x = -5 ========== Cheers, Stan H.
 Percentage-and-ratio-word-problems/158309: Anna has 6 liters of 60% acid. How much water should she add to make a solution that is 40% acid?1 solutions Answer 116666 by stanbon(57282)   on 2008-09-21 23:27:32 (Show Source): You can put this solution on YOUR website!Anna has 6 liters of 60% acid. How much water should she add to make a solution that is 40% acid? --------------------- Acid Equation: 0.6*6 + 0*x = 0.4(6+x) 0.36 = 0.24 + 0.4x 0.4x = 0.12 x = 3 liters (amount of water that must be added) ----------- Cheers, Stan H.
 Geometry_Word_Problems/156936: This question is from textbook PRECALCULUS Mathmatics for Calculus 4th I can't figure out how to even start this: The hypotenuse of a right triangle has length 20 cm. The sum of the lengths of the other two sides is 28 cm. Find the lengths of the other two sides of the triangle.1 solutions Answer 115705 by stanbon(57282)   on 2008-09-14 19:17:01 (Show Source): You can put this solution on YOUR website!Let one of the sides be "x"; Let the other side be "28-x' Use Pythagoras to find "s" and 28-x: EQUATION: x^2 + (28-x)^2 = 20^2 x^2 + 784 - 56x + x^2 = 400 2x^2 -56x + 384 = 0 x^2 - 28x + 192 = 0 (x-12)(x-16) = 0 x = 12 or x = 16 ----------- Cheers, Stan H.
 expressions/156695: How do I solve for x in the following: (x x x) - 3 = 8x (the xxx in paranthesis is x times x times x) thank you! (it is a teacher created homework problem and not a problem in text. Even looked in text trying to find a model problem and could not. We are in the Mcdougal Littel Algebra 1 book.)1 solutions Answer 115565 by stanbon(57282)   on 2008-09-13 18:03:43 (Show Source): You can put this solution on YOUR website!solve for x in the following: (x x x) - 3 = 8x x^3 -8x -3 = 0 ------------ I graphed it and found it crossed the x-axis at 2.148177... --------------- Cheers, Stan H.
 Radicals/156659: 3^x-5=31 solutions Answer 115481 by stanbon(57282)   on 2008-09-13 07:45:14 (Show Source): You can put this solution on YOUR website! 3^(x-5) = 3 ----------------- Since the bases are the same, the exponents must be equal: x-5 = 1 x = 6 =========== Cheers, Stan H.
 expressions/156502: This question is from textbook Algebra x^2+3x+2 x^2+5x+4 ________ / _________ x^2+7x+12 x^2+5x+61 solutions Answer 115480 by stanbon(57282)   on 2008-09-13 07:17:27 (Show Source): You can put this solution on YOUR website!x^2+3x+2 x^2+5x+4 ________ / _________ x^2+7x+12 x^2+5x+6 ------------------------------ Factor where you can to get: (x+2)(x+1) (x+4)(x+1) ________ / _________ (x+3)(x+4) (x+3)(x+2) -------------------------------- Invert the denominator and change to multiplication: (x+2)(x+1) (x+3)(x+2) ________ * _________ (x+3)(x+4) (x+4)(x+1) --------------------------------- Cancel factors that are common to a numerator and denominator, such as (x+1), (x+3) (x+2) (x+2) ________ * _________ (x+4) (x+4) -------------------------------- = (x+2)^2 / (x+4)^2 ========================= Cheers, Stan H.