SOLUTION: Add the following rational expressions and make sure you answer is simplified: x^3-x^2-10x/x^2-8x+16 + -3x^2-6x+64/x^2-8x+16 = What I have so far is: x^3-x^2-10x >> x(x^2-x-1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Add the following rational expressions and make sure you answer is simplified: x^3-x^2-10x/x^2-8x+16 + -3x^2-6x+64/x^2-8x+16 = What I have so far is: x^3-x^2-10x >> x(x^2-x-1      Log On


   

Question 82586: Add the following rational expressions and make sure you answer is simplified:
x^3-x^2-10x/x^2-8x+16 + -3x^2-6x+64/x^2-8x+16 =
What I have so far is: x^3-x^2-10x >> x(x^2-x-10) [here is where I got stuck]
x^2-8x+16 >> (x-4)(x-4)
x^2-8x+16 >> (x-4)(x-4)
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
[x^3-x^2-10x/x^2-8x+16] + [-3x^2-6x+64/x^2-8x+16]
The denominators are the same so combine the numerators:
= [ x^3-4x^2-16x+64]/[(x-4)^2]
= [x^2(x-4)-16(x-4)]/[(x-4)^2]
= [(x-4)(x^2-16)]/[(x-4)^2
= [ (x-4)^2(x+4)]/[(x-4)^2]
Cancel the (x-5)^2 factors to get:
= x+4
==============
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Add the following rational expressions and make sure you answer is simplified:
%28x%5E3-x%5E2-10x%29%2F%28x%5E2-8x%2B16%29 + %28-3x%5E2-6x%2B64%29%2F%28x%5E2-8x%2B16%29 =
:
They have the same denominators so write it:
%28%28x%5E3-x%5E2-10x%29+%2B+%28-3x%5E2-6x%2B64%29%29%2F%28x%5E2-8x%2B16%29
:
%28x%5E3-x%5E2-10x+-+3x%5E2-6x%2B64%29%2F%28%28x-4%29%28x-4%29%29: remove brackets, factor denominator as you did
:
%28x%5E3+-+x%5E2+-+3x%5E2+-+10x+-+6x+%2B+64%29%2F%28%28x-4%29%28x-4%29%29; group like terms
:
%28x%5E3-4x%5E2-16x%2B64%29%2F%28%28x-4%29%28x-4%29%29; combined like terms
:
%28x%5E2%28x-4%29-16%28x-4%29%29%2F%28%28x-4%29%28x-4%29%29; group and factor
:
%28%28x-4%29%28x%5E2-16%29%29%2F%28%28x-4%29%28x-4%29%29; factor out (x-4)
:
%28%28x-4%29%28x-4%29%28x%2B4%29%29%2F%28%28x-4%29%28x-4%29%29: (x^2-16) can be factored (difference of squares)
:
Cancel out both (x-4)'s and you have:
x + 4