Questions on Algebra: Rational Functions, analyzing and graphing answered by real tutors!

Tutors Answer Your Questions about Rational-functions (FREE)

Question 260080: Simplifying Complex Fractions. I know the LCD is S, but I am not sure about how to determine the LCD with exponents. Example problem I am working on right now.
2/s - 2/s^2
___________
4/s^3 + 4/s^2
Click here to see answer by richwmiller(9135)

Question 260265: If h(x)=h(x-1) + 4x and h(3) = -17, then find h(7). Please help!
Click here to see answer by richwmiller(9135)

Question 260305: If f(4)=0 and f(6)=6, what represents f(x)?
Click here to see answer by drk(1908)

Question 260502: For the functions f(x) and g(x), determine the domain of (fg)(x) (the product of f and g). f(x)=2/x-12, g(x)=-6x-5.
a) x is a real number.
b) x is a real number and x is not equal to 5.
c) x is a real number and x is not equal to -12.
d) x is a real number and x is not equal to 12.
If my understanding is correct, the answer would be option a. Is this correct? Please explain.
Click here to see answer by drk(1908)

Question 260511: How many solutions exist for the equation
Click here to see answer by drk(1908)

Question 260553: -15 / x = x+16/ 4
Click here to see answer by unlockmath(1599)

Question 260672: Hi :o)
This is actually a calculus question but it's the fractional algebra stuff that I'm still a little unsure of. I was hoping someone might let me know if I'm on the right track with this question:
The amount n (in g) of a compound formed during a chemical change is n=8t/(2t²+3), where t is the time (in s). Find dn/dt for t=0.5 s using the quotient rule.
My try:
u = 8t v = 2t²+3
du/dx = 8 dv/dx = 4t
dn/dt =[(2t²+3)(8) – (8t)(4t)]/ (2t²+3)²

=[(16t²+24) – (32t²)]/(2t²+3)²
=(-16t²+24)/(2t²+3)²
=[8(-2t²+3)]/(2t²+3)²
substituting t=0.5, my answer was 1.63g/s.
Am I close?
Thanks so much for you help :o)

Click here to see answer by jsmallt9(3296)

Question 260674: Hi :o)
This is another calculus question but again it's the fractional algebra stuff that I'm unsure of.:
Differentiate
y = (5x³ + 7x)^1/4
I managed to get to the point of
dy/dx = 1/4(15x³ + 7)/(5x³ + 7x)^3/4
but not sure if it's right or if I can go any further than this answer.
Thanks again!
manda
Click here to see answer by Fombitz(13828)

Question 260737: Can someone help me with the following homework question I have to answer? Thank you.
A high school class wants to raise money by recycling newspapers. The class decided to rent a truck at a cost of $150 for the week. The market price for recycled newspapers is $15 per ton. Write an equation representing the amount of money the class will make based on the number of tons of newspaper collected. Explain what you did to get your answer.
Click here to see answer by jim_thompson5910(28536)

Question 260736: Can someone help me with the following homework question I have to answer? Thank you.
Bill is paid hourly. If he works 8 hours he will receive $50. Write an equation for his salary based on the number of hours he works. Explain what you did to get your answer.
Click here to see answer by jim_thompson5910(28536)

Question 260676: Hi :o)
Last calculus question if anyone can help???
Find derivative of y = (x-1)³(x²-2)²
I thought I'd need to use both the product and chain rules, so tried;
u=(x-1)³ du^n/dx=3(x-1)²(1)
v=(x²-2)² dv^n/dx=2(x²-2)^1(2x)
= {(x-1)³[3(x-1)²(1)]} + {(x²-2)²[2(x²-2)^1(2x)]}
= [(x-1)³3(x-1)²] + [(x²-2)²4x(x²-2)]
= 3(x-1)^5 + 4x(x²-2)^3
...does that look right? Can I go further?
Thanks so, so much again :o)
Click here to see answer by jim_thompson5910(28536)

Question 260750: From a 24-inch by 24-inch piece Of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express the volume as a function of x. Graph the function and from the graph determine the value of x, to the nearest tenth of an inch, that will yield the maximum volume.
I know that volume is a product of width x length x height, but I'm not sure how to express this as a function of x. Can someone please explain this to me?
Click here to see answer by drk(1908)

Question 260910: A plane can fly 160 mph in calm air. Flying with the wind, the plane can fly 500 miles in the same amount of time required to fly 420 miles against the wind. What is the speed of the plane? ok so the answer is supposed to be 13.9 mph but i don't know how to set up me equations.
Click here to see answer by Greenfinch(383)

Question 260936: Adding and Subtracting Rational Expressions. Help please!
2x+1/x^2-2x+3-x/5x-20.
How do I factor out the denominators. Where do I go from there?
Click here to see answer by richwmiller(9135)

Question 260945: 2x+1 over (x^2-2x) + 3-x over (5x^2-20)
Adding and Subtracting rational expressions. Denominators are in ()
Click here to see answer by drk(1908)

Question 261288: The rational function M(t) = (0.5t+400)/(0.04t^2+1) models the number of milligrams of medication in the bloodstream of a patient t hours after 400 milligrams of the medication have been injected into the patient’s bloodstream.
(a) Find M(5) and M(10). Round to the nearest milligram.
(b) What will M approach as t = ∞ ?

Click here to see answer by stanbon(57290)

Question 261325: f(x)=5x/(x+1)
Click here to see answer by stanbon(57290)

Question 261440: if h(x)=2x-b/3x+4 and h(2)=1/2, what is the value of b? im really stuck on this problem and one more almost the same. i vaguely remember how to do it, but i cant remember the whole process...
Click here to see answer by jim_thompson5910(28536)

Question 261446: Explain in detail one application of derivatives
Click here to see answer by stanbon(57290)

Question 261600: a bookstore sells paperbacks, hardbacks, and magazines. For every three paperbacks sold, five hardbacks are also sold. For every ten hardbacks sold, twenty magazines are sold.
Click here to see answer by richwmiller(9135)

Question 261554: 8.5 x 2/5
Click here to see answer by edjones(7569)

Question 261666: if a circular table is to be made that will have a top covered with material that costs $3.50 per square foot. The covering is to cost no more than $60. What is the maximum radius for the top of the table?
Click here to see answer by mananth(12270)

Question 261746: (2x^3+x^2-3x)/(x^3-x^2)
Click here to see answer by jim_thompson5910(28536)

Question 261745: r(x)= x+4 over x+2
i need to find the x intercept and vertical asymptotes
Click here to see answer by solver91311(16877)

Question 262096: graph the equation 4x+3y=-12
Click here to see answer by richwmiller(9135)

Question 262297: Let ƒ(x) = 3x2 – 2x and g(x) = x – 6. Find each value.
(ƒ – g)(2)
Click here to see answer by nerdybill(6957)

Question 262325: Could you help me get started on this problem? I am super confused..
Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.
29. through (1,9); perpendicular to x=5
Please help me! lol :)
Click here to see answer by richwmiller(9135)

Question 262553: How is doing operation (add, subtract, multipy, and divide) with rational expressions similar to or different from doing operations with fractions?
Click here to see answer by drk(1908)

Question 262585: How do you find the answer to x-a/a-x?
Click here to see answer by richwmiller(9135)

Question 263098: How do you graph the following function: y=-x^2 + 2x
How do I find x and y intercepts?
Thank you for any help
Click here to see answer by jim_thompson5910(28536)

Question 263004: f(x)=-x^2-2x+7
find the vertex and axis of symmetry and graph the function
Click here to see answer by checkley77(12569)

Question 263260: A rectangular room has an area of 252 square ft.
The length of the room is 4 feet more than its width. Find the dimensions of the room.

Click here to see answer by richwmiller(9135)

Question 263622: HELLO! Can you please help me solve this problem? (8/x)-(3/x)=(6/x-1)
Thank you!!!
Click here to see answer by drk(1908)

Question 263635: How about (3x-21)/(3x)divided by(x^2-49)/(x^2+7x)
Click here to see answer by drk(1908)

Question 263646: How about these? (3x-2)/(x+1)+(2x-3)/(2x-1)

(5x)/(4x^2)+7/(x+1)
Thanks so much!!!
Click here to see answer by drk(1908)

Question 263712: what is (4x-1) to the 1/2 power = 3 find x
Click here to see answer by richwmiller(9135)

Question 263712: what is (4x-1) to the 1/2 power = 3 find x
Click here to see answer by mananth(12270)

Question 263731: find x-cordinates
f(x)=-2x^2+2x+9
Click here to see answer by JBarnum(2044)

Question 263760: -/ = sqrt
1. 7+ -/(2x - 1) = 10
2.4(x - 9)^1/3 =8
3. -/(2x - 1) = x - 8
4. (4x + 3)^2/3 = (16x + 44)^1/3
5. A circular table is to be made that will have a top covered with material that costs $3.50 per square foot. The covering is to cost no more than $60. What is the maximum radius for the top of the table? (1 point)
Click here to see answer by JBarnum(2044)

Question 263671: 5z/z-2 - 10/z+2 = 40/z^2 -4
Click here to see answer by JBarnum(2044)

Question 263671: 5z/z-2 - 10/z+2 = 40/z^2 -4
Click here to see answer by jsmallt9(3296)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055