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Recent problems solved by 'stanbon'

stanbon answered: 57151 problems
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, >>Next

Quadratic_Equations/476857: The revenue from selling x units of a product is given by y = -0.0002x^2 + 20x. How many units must be sold in order to have the greatest revenue? (Find the x-coordinate of the vertex of the parabola.) 1 solutions Answer 326940 by stanbon(57219)   on 2011-08-01 19:17:44 (Show Source): You can put this solution on YOUR website! The revenue from selling x units of a product is given by y = -0.0002x^2 + 20x. How many units must be sold in order to have the greatest revenue? (Find the x-coordinate of the vertex of the parabola.) ----- maximum revenue occurs when x = -b/(2a) = -20/(2*-0.0002) = 50,000 ------------------------- Cheers, Stan H.

Subset/476861: Given the following sets, select the statement below that is true. A = {l, a, t, e, r}, B = {l, a, t, e}, C = {t, a, l, e}, D = {e, a, t} (Points : 2) B ⊆ C and C ⊆ B A ⊂ B and D ⊂ A D ⊆ B and A ⊆ D D ⊆ B and B ⊆ D A ⊆ C and D ⊂ A 1 solutions Answer 326939 by stanbon(57219)   on 2011-08-01 19:14:25 (Show Source): You can put this solution on YOUR website! Given the following sets, select the statement below that is true. A = {l, a, t, e, r}, B = {l, a, t, e}, C = {t, a, l, e}, D = {e, a, t} (Points : 2) B ⊆ C and C ⊆ B::::true A ⊂ B and D ⊂ A:fakse D ⊆ B and A ⊆ D:false D ⊆ B and B ⊆ D:false A ⊆ C and D ⊂ A:false =========================== Cheers, Stan H.

Rectangles/476860: determine the length of the diagonal of a square if its area is 256 units 1 solutions Answer 326935 by stanbon(57219)   on 2011-08-01 19:09:14 (Show Source): You can put this solution on YOUR website! determine the length of the diagonal of a square if its area is 256 units ----- Area of a square = side^2 --- s^2 = 256 s = sqrt(256) = 16 ---- diagonal = sqrt[16^2 + 16^2] = sqrt(2*16^2] = 4*sqrt(2) units ======================== Cheers, Stan H. ========================

Equations/476830: A regular slice of pizza is $.75 and a hamburger slice is $1.35. We sold 40 more regular slices than hamburger slices. Our total was $292.50. How many hamburger slices did we sell. 1 solutions Answer 326933 by stanbon(57219)   on 2011-08-01 18:58:18 (Show Source): You can put this solution on YOUR website! A regular slice of pizza is $.75 and a hamburger slice is $1.35. We sold 40 more regular slices than hamburger slices. Our total was $292.50. How many hamburger slices did we sell. ------------------------------------- Let # of hamburger slices be h Then # of pizza slices is h+40 Value Eq:: 75(h+40)+135h = 29250 cents 210h + 75*40 = 29250 h = $1.25 (price of one hamburger slice) =================== Cheers, Stan H. ----------------------------------------

Polynomials-and-rational-expressions/476824: x^-2y^-5 ____________ Divided by -4x^4y^-3 1 solutions Answer 326926 by stanbon(57219)   on 2011-08-01 18:29:36 (Show Source): You can put this solution on YOUR website! (x^-2y^-5) / (-4x^4y^-3) ================ = (1/-4)(x^-2/x^4)(y^-5/y^-3) ----- = (-1/4)(1/x^6)(1/y^2) ------------------ = -1/(x^6*y^2) ==================== Cheers, Stan H. =================

Polynomials-and-rational-expressions/476823: simplify the algebraic expression (2k^3)^0 / 8 1 solutions Answer 326922 by stanbon(57219)   on 2011-08-01 18:21:01 (Show Source): You can put this solution on YOUR website! simplify the algebraic expression (2k^3)^0 / 8 ------- The zero power of anything (except 0) is "1". --- Ans: 1/8 ============= Cheers, Stan H.

Parallelograms/476822: I need help proving this theorem using a formal proof. If two inscribed angles intercept the same arc, then the angles are congruent. 1 solutions Answer 326920 by stanbon(57219)   on 2011-08-01 18:18:36 (Show Source): You can put this solution on YOUR website! Please check out the following site: ------ http://www.cliffsnotes.com/study_guide/Arcs-and-Inscribed-Angles.topicArticleId-18851,articleId-18825.html --------- Cheers, Stan H.

Polynomials-and-rational-expressions/476808: divide and simplify 3v-24/77 divided by v-8/35v these are 2 seperate fractions: 3v-24 on top and 77 on bottom, same with the other one 1 solutions Answer 326917 by stanbon(57219)   on 2011-08-01 18:08:57 (Show Source): You can put this solution on YOUR website! [3v-24/77] / [v-8/35v] ---- Invert the denominator and multiply to get: [3v-24/77] * [35v/v-8] ---- [3(v-8)/77] * [35v/(v-8) --- Cancel the (v-8)factors Cancel the common "7" factors ---- = [3/11] * [5v/1] ----- = 15v/11 ======================= Cheers, Stan H. =======================

Probability-and-statistics/476746: 1. For a particular sample of 65 scores on a psychology exam, the following results were obtained. First quartile = 42 Third quartile = 77 Standard deviation = 10 Range = 68 Mean = 65 Median = 68 Mode = 71 Midrange = 65 Answer each of the following: I. What score was earned by more students than any other score? Why? II. What was the highest score earned on the exam? III. What was the lowest score earned on the exam? IV. According to Chebyshev's Theorem, how many students scored between 45 and 85? V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 35 and 95? Please show all of your work. Thank you so much 1 solutions Answer 326908 by stanbon(57219)   on 2011-08-01 17:19:06 (Show Source): You can put this solution on YOUR website! 1. For a particular sample of 65 scores on a psychology exam, the following results were obtained. First quartile = 42 Third quartile = 77 Standard deviation = 10 Range = 68 Mean = 65 Median = 68 Mode = 71 Midrange = 65 Answer each of the following: I.What score was earned by more students than any other score? Why?:::mode = 71 --------------------- II. What was the highest score earned on the exam?::Mean+34 = 65+34 = 99 --------------------- III. What was the lowest score earned on the exam?:::Mean-34 = 65-34 = 31 ------------------------ IV. According to Chebyshev's Theorem, how many students scored between 45 and 85?:::P(mean-2std) = (1/2)0.75 = 37.5% ------------------------ V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 35 and 95? z(35) = (35-65)/10 = -3 Z(95) = (95-65)/10 = +3 --- P(35< x < 95) = P(-3 < z < 3) = 0.9973 ========================================= Cheers, Stan H.

Probability-and-statistics/476779: Binomial distribution with n=6 and p=0.2 find; a) P(x=0) 1 solutions Answer 326906 by stanbon(57219)   on 2011-08-01 17:09:20 (Show Source): You can put this solution on YOUR website! Binomial distribution with n=6 and p=0.2 find; a) P(x=0) = binompdf(6,0.2,0) = 0.2621 --- Cheers, Stan H.

Probability-and-statistics/476769: The mean score on a history test was 74.3 and the standard deviation was 5.7. Assuming the scores are normally distributed,what fraction of scores are above 80? 1 solutions Answer 326904 by stanbon(57219)   on 2011-08-01 17:06:40 (Show Source): You can put this solution on YOUR website! The mean score on a history test was 74.3 and the standard deviation was 5.7. Assuming the scores are normally distributed,what fraction of scores are above 80? ---- z(80) = (80-74.3)/5.7 = 1 --- P(x > 80) = P(z > 1) = normalcdf(1,100) = 0.1587 --------------- Cheers, Stan H. ==============

Probability-and-statistics/476776: An often-quoted example of an event of extremely low probability is that a monkey types Shakespeare’s entire play Hamlet by randomly striking keys on a typewriter. Assume that the typewriter has 48 keys (including the space bar) and that the monkey is equally likely to hit any key. A. Find the probability that such a monkey will actually correctly type just the title of the play as his first word. B. What is the probability that the monkey will type the phrase “To be or not to be” as his first words? thankyou :) 1 solutions Answer 326897 by stanbon(57219)   on 2011-08-01 17:01:38 (Show Source): You can put this solution on YOUR website! An often-quoted example of an event of extremely low probability is that a monkey types Shakespeare’s entire play Hamlet by randomly striking keys on a typewriter. Assume that the typewriter has 48 keys (including the space bar) and that the monkey is equally likely to hit any key. Ans: (1/26)^6 = 3.2371x10^-9 --------------------------------------- A. Find the probability that such a monkey will actually correctly type just the title of the play as his first word. B. What is the probability that the monkey will type the phrase “To be or not to be” as his first words? Ans: (1/26)^(13) = 4.0304x10^-19 ----------------------------------------- Cheers, Stan H. ===========

test/476736: 3 workers take 10 days to make a boat. How long would 5 workers take. 1 solutions Answer 326880 by stanbon(57219)   on 2011-08-01 15:17:13 (Show Source): You can put this solution on YOUR website! 3 workers take 10 days to make a boat. How long would 5 workers take. --- # of workers an # of days are inversely related. ---- d = k/w -- Solve for "k" using "3 workers take 10 days to make a boat". 10 = k/3 k = 30 ----- Equation: d = 30/w --- How long would 5 workers take. d = 30/5 d = 6 days (# of days for 5 workers to do the job) ---- Cheers, Stan H.

Permutations/476730: use the combinations formula to write an expression for the number of line segments that join pairs of verticies on an n-sided polygon. use your result from part (a) to write formula for the numbber of diagonals of an n-sided convex polygon. 1 solutions Answer 326878 by stanbon(57219)   on 2011-08-01 15:13:24 (Show Source): You can put this solution on YOUR website! use the combinations formula to write an expression for the number of line segments that join pairs of verticies on an n-sided polygon. Ans: nC2 = [n(n-1)]/(1*2) = (n/2)(n-1) ------------------------------------------------- use your result from part (a) to write formula for the number of diagonals of an n-sided convex polygon. --- n of the lines from (a) are sides of the polygon. # of diagonals is (n/2)(n-1)-n ------------------------------------- cheers, Stan H.

test/476723: Please help me. I'm really confused. Describe the locus of points in space 3 inches from a given point P. 1 solutions Answer 326876 by stanbon(57219)   on 2011-08-01 15:09:59 (Show Source): You can put this solution on YOUR website! Please help me. I'm really confused. Describe the locus of points in space 3 inches from a given point P. ---- In 3-D space the locus is a sphere with radius = 3 inches and center at P. ----------- In 2-D is would be a circle with radius = 3 inches and center at P. ============== Cheers, Stan H.

Money_Word_Problems/476726: How do I find out how many months it will take me to double my money at 5%APR? What is the formula? Thank you. 1 solutions Answer 326875 by stanbon(57219)   on 2011-08-01 15:07:35 (Show Source): You can put this solution on YOUR website! How do I find out how many months it will take me to double my money at 5%APR? What is the formula? 2Ao = Ao(1+(r/n))^(nt) --- Ao is the amt you invest. r = 5% n is the number of times per year you compound the money t is the number of years. --- Example: Say you compound quadterly (4 times per year). 2Ao = Ao(1+(0.05/4))^(4t) --- 2 = (1.0125)^(4t) --- Take the log of both sides to get: 4t = log(2)/log(1.0125) 4t = 55.8 t = 13.94 years = 12*13.94 = 167.39 months ============================================== cheers, Stan H. ============

Quadratic-relations-and-conic-sections/476727: Put the equation in standard form for an ellipse 100x^2-200x+9y^2+18y=791 1 solutions Answer 326873 by stanbon(57219)   on 2011-08-01 14:58:55 (Show Source): You can put this solution on YOUR website! Put the equation in standard form for an ellipse 100x^2-200x+9y^2+18y=791 ---------------- 100(x^2-2x+1) + 9(y^2+2y+1) = 791+100+9 --- 100(x-1)^2 + 9(y+1)^2 = 900 --- (x-1)^2/9 + (y+1)^2/100 = 1 ----------------------------------- cheers, Stan H. ============

Exponents/476715: I was asked to describe three rules for exponents and came up with the following: Product Rule – When multiplying numbers with the same base we add the exponents together Quotient Rule – When dividing numbers with the same base we keep the base, subtracting the exponent of the denominator from the exponent of the numerator Power Rule – This is where we raise the base and multiply the exponents Will those descriptions suffice? Also can you please provide me with an example of an expression that uses scientific notation and at least one of the rules for exponents that I have described? Please and thank you. 1 solutions Answer 326869 by stanbon(57219)   on 2011-08-01 14:52:18 (Show Source): You can put this solution on YOUR website! I was asked to describe three rules for exponents and came up with the following: Product Rule – When multiplying numbers with the same base we add the exponents together. Good ----------------------- Quotient Rule – When dividing numbers with the same base we keep the base, subtracting the exponent of the denominator from the exponent of the numerator I would say: "Subtract the smaller exponent from the larger exponent". ----------------------- Power Rule – This is where we raise the base and multiply the exponents I would say: We raise the base to a power equal to the product of the exponents. ------------------------ Also can you please provide me with an example of an expression that uses scientific notation and at least one of the rules for exponents that I have described? (3.2x10^2)/(1.6x10^5) = (3.2/1.6)(10^2/10^5) = 2*10^(-3) = 0.002 ================================= Cheers, Stan H.

Matrices-and-determiminant/476719: EVALUATE X-3/X^2-9 1 solutions Answer 326864 by stanbon(57219)   on 2011-08-01 14:37:47 (Show Source): You can put this solution on YOUR website! EVALUATE X-3/X^2-9 ------ (x-3)/[(x-3)(x+3)] ---- Cancel the common (x-3) factor to get: = 1/(x+3) ================== Cheers, Stan H. ------------

real-numbers/476717: Is the number 2.03003000300003... where the pattern of adding another 0 before the next 3 continues forever rational or irrational? I recognize there is a pattern so my feeling is that it is rational. However if it is rational I should be able to turn it into a fraction with an integer as numerator and a nonzero integer in the denominator. Am I right and is the process of converting difficult? 1 solutions Answer 326863 by stanbon(57219)   on 2011-08-01 14:35:01 (Show Source): You can put this solution on YOUR website! It is a pattern, but it is not a repeating pattern. No interval of digits repeats endlessly. -- Therefore the number is not rational. Cheers, Stan H. =======

Linear-systems/476706: can you help me answer 8-5r over 6=3, -4a-1 over -10a=3/8, and y+4 over y-1=4/3 -thanks 1 solutions Answer 326858 by stanbon(57219)   on 2011-08-01 14:07:07 (Show Source): You can put this solution on YOUR website! 8-5r over 6=3, (8-5r)/6 = 3 (8-5r) = 18 -5r = 10 r = -2 ------------------------- -4a-1 over -10a=3/8, (-4a-1)/10a = (3/8) Cross-multiply: -32a - 8 = -30a 2a = -8 a = -4 ========================= y+4 over y-1=4/3 --- (y+4)/(y-1) = 4/3 --- 3y+12 = 4y-4 y = 16 ----------------- Cheers, Stan H.

Radicals/476703: sqrt3 (8 sqrt5 - 4 sqrt 4)How do I solve this using the distributive property? I keep getting the wrong answer! 1 solutions Answer 326857 by stanbon(57219)   on 2011-08-01 14:00:17 (Show Source): You can put this solution on YOUR website! sqrt3 (8 sqrt5 - 4 sqrt 4) How do I solve this using the distributive property? ------------- = (sqrt(3))(8sqrt(5) - (sqrt(3))(4sqrt(4)) ---- = 8sqrt(15) - 4sqrt(12) --- = 8sqrt(15) - 4*2*sqrt(3) --- = 8sqrt(15) - 8sqrt(3) ---- = 8[sqrt(15)-sqrt(3)] ========================= cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/476700: i need help with factoring because i forgot it my 8th grade year and this is my homework over the summer. 33. 5a to the second power b o the second power c-15abc to the second power. 34. x to the second power -7x+6. 35. 2r to the second power -3r-20. -Thanks 1 solutions Answer 326856 by stanbon(57219)   on 2011-08-01 13:55:42 (Show Source): You can put this solution on YOUR website! 33. 5a to the second power b to the second power c-15abc to the second power. --- 5a^2*b^2*c - 15abc^2 --- Common Factor: 5abc --- Factor Form: = 5abc[ab - 3c] ==================================== 34. x to the second power -7x+6. . --- x^2-7x+6 = (x-6)(x-1) ---================================ 35. 2r to the second power -3r-20 2r^2 - 3r - 20 --- = 2r^2-8r+5r-20 --- = 2r(r-4)+5(r-4) --- = (r-4)(2r+5) ================= Cheers, Stan H. =================

Radicals/476694: How do you solve the problem 1 diveded by the square root of 2? 1 solutions Answer 326854 by stanbon(57219)   on 2011-08-01 13:48:05 (Show Source): You can put this solution on YOUR website! How do you solve the problem 1 diveded by the square root of 2? ---- You want to rationalize the denominator: (1/sqrt(2) = ? --- Multiply numerator and denominator by sqrt(2) to get: ---- sqrt(2)/2 OR (1/2)sqrt(2) --- Notice that the denominator is no longer an irrational number. Cheers, Stan H.

test/476683: find the sum of infinite geometric series 7 + 3 + 9/7 1 solutions Answer 326849 by stanbon(57219)   on 2011-08-01 13:15:20 (Show Source): You can put this solution on YOUR website! find the sum of infinite geometric series 7 + 3 + 9/7 ---- a = 7 r = 3/7 --- Sum = a/(1-r) = 7/(4/7) = 49/4 = 12.25 ========================= Cheers, Stan H.

Probability-and-statistics/476671: 1. What is the probability of a Heart, given less than 7? 2. Are the events "King" and "less than 7" mutually exclusive? why or why not? 3. Are the events "Heart" and "less than 7" independent? why or why not? make sure you show this using the formula definition. 1 solutions Answer 326848 by stanbon(57219)   on 2011-08-01 13:10:48 (Show Source): You can put this solution on YOUR website! 1. What is the probability of a Heart, given less than 7? = P(heart AND <7)/P(<7) = 0/(20/52) = 0 --------------------------------------------- 2. Are the events "King" and "less than 7" mutually exclusive? why or why not? Yes because no card is a King and less than 7 ------------------------------------------- 3. Are the events "Heart" and "less than 7" independent? why or why not? make sure you show this using the formula definition. No because there are cards that are King and are Heart. ---------------- Cheers, Stan H. ==============

Probability-and-statistics/476672: 1. ninety percent of licensed practical nurses are women (statistical abstract of the united states, 1992). suppose 10 licensed practical nurses are randomly selected. A. what is the mean and standard devition? B. what is the probability that three of the licensed practical nurses will be women? C. what is the probability that at most 9 will be women? D. If in fact only 3 are women, what conclusions could you draw? 1 solutions Answer 326846 by stanbon(57219)   on 2011-08-01 13:07:15 (Show Source): You can put this solution on YOUR website! 1. ninety percent of licensed practical nurses are women (statistical abstract of the united states, 1992). suppose 10 licensed practical nurses are randomly selected. A. what is the mean and standard devition? mean = np = 10*0.9 = 9 sqrt(npq) = sqrt(9*0.1) = 0.9487 --------------- B. what is the probability that three of the licensed practical nurses will be women?:::P(x=3) = 10C3(0.9)^3*0.1^7 = 120*0.729*0.0000001 = 0.00000875 ------------------ C. what is the probability that at most 9 will be women? P(0<= x <=9) = binomcdf(10,0.9,9) = 0.6513 ------------------ D. If in fact only 3 are women, what conclusions could you draw? I'll leave that to you. Cheers, Stan H.

test/476674: What is the minimum product of two numbers whose difference is 6? What are the numbers? 1 solutions Answer 326845 by stanbon(57219)   on 2011-08-01 12:51:27 (Show Source): You can put this solution on YOUR website! What is the minimum product of two numbers whose difference is 6? ------ x - y = 6 So x = y+6 ----- product = xy = (y+6)y = y^2+6y --- You have a quadratic equation: y^2 + 6y = Product ---- The mimimum occurs when y = -b/(2a) = -6/(2*1)= -3 --- Solve for "x": x = y+6 x = -3+6 = 3 ---- Minimum product = xy = 3*-3 = -9 ==================================== Cheers, Stan H. ====================================

real-numbers/476667: solve |m|= 4 over the set of real numbers 1 solutions Answer 326844 by stanbon(57219)   on 2011-08-01 12:43:48 (Show Source): You can put this solution on YOUR website! solve |m|= 4 over the set of real numbers --- m = 4 or -4 ------------- Cheers, Stan H.

Probability-and-statistics/476665: 1. One card is choesen from a standard deck. a. what is the probability of less than 7 (Ace high)? i really need help for this question. 1 solutions Answer 326830 by stanbon(57219)   on 2011-08-01 12:08:17 (Show Source): You can put this solution on YOUR website! One card is choesen from a standard deck. a. what is the probability of less than 7 There are 5 cards less than 7 in each of 4 suits = 28 cards --- P(less than 7) = 28/52 = 19/26 ============= Cheers, Stan H.

Functions/476657: Given f(x) = and g(x) = Find (fog)(x). Any help would be appreciated! Thank you! 1 solutions Answer 326828 by stanbon(57219)   on 2011-08-01 12:04:09 (Show Source): You can put this solution on YOUR website! Given f(x) = (x-3)/(x-1) and g(x) = (x-4)/(x-2) --------- Find (fog)(x) = f[g(x)] = f[(x-4)/x-2)] --- = [[(x-4)/(x-2)]-4]/[[(x-4/(x-2)] -2] ----------- = [(x-4-4(x-2))/(x-2)]/[(x-4-2(x-2)/(x-2)] --- = [-3x+4]/[-x] --- = (3x-4)/x =============== Cheers, Stan H.