SOLUTION: Would somebody help me reduce expression to lowest terms? it's this one here: x^2-4/8-x^3 Thanks in advance!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Would somebody help me reduce expression to lowest terms? it's this one here: x^2-4/8-x^3 Thanks in advance!      Log On


   

Question 1140376: Would somebody help me reduce expression to lowest terms? it's this one here:
x^2-4/8-x^3
Thanks in advance!
Found 2 solutions by Boreal, ankor@dixie-net.com:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
this is (x+2)(x-2) for numerator, difference of squares
divided by (2-x)(4+2x+x^2) difference of cubes
The x-2 cancels IF we multiply the denominator by -1 and the whole fraction by -1.
Then we have -(x+2)/(4+2x+x^2)
The second - turns (2-x) into (x-2), which can cancel.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-4%29%2F%288-x%5E3%29
:
%28x%5E2-4%29%2F%282%5E3-x%5E3%29
The denominator is the difference of cubes, which factors
%28%28x-2%29%28x%2B2%29%29%2F%28%282-x%29%284%2B2x%2Bx%5E2%29%29
factor out -1 in the denominator
%28-1%28x-2%29%28x%2B2%29%29%2F%28-1%28x-2%29%284%2B2x%2Bx%5E2%29%29
cancel (x-2)
%28%28x%2B2%29%29%2F%28-1%284%2B2x%2Bx%5E2%29%29 = -%28%28x%2B2%29%29%2F%28%284%2B2x%2Bx%5E2%29%29