SOLUTION: Please help me simplify this rational expression: {{{ ((x^3+y^3)/(2x^3+2x^2y))/((3x^3-3x^2y+3xy^2)/(6x^2-6y^2))}}}

Algebra ->  Rational-functions -> SOLUTION: Please help me simplify this rational expression: {{{ ((x^3+y^3)/(2x^3+2x^2y))/((3x^3-3x^2y+3xy^2)/(6x^2-6y^2))}}}      Log On


   

Question 196861: Please help me simplify this rational expression:
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: the previous solution has a sign error and the answer should be much simpler.



Start with the given expression.


Multiply the first fraction %28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29 by the reciprocal of the second fraction %283x%5E3-3x%5E2y%2B3xy%5E2%29%2F%286x%5E2-6y%5E2%29.


Factor x%5E3%2By%5E3 to get %28x%2By%29%28x%5E2-xy%2By%5E2%29.


Factor 2x%5E3%2B2x%5E2y to get 2x%5E2%28x%2By%29.


Factor 6x%5E2-6y%5E2 to get 6%28x-y%29%28x%2By%29.


Factor 3x%5E3-3x%5E2y%2B3xy%5E2 to get 3x%28x%5E2-xy%2By%5E2%29.


Combine the fractions.


Multiply 2x%5E2 and 3x to get 6x%5E3.


Highlight the common terms.


Cancel out the common terms.


%28%28x-y%29%28x%2By%29%29%2F%28x%5E3%29 Simplify


%28x%5E2-y%5E2%29%2F%28x%5E3%29 FOIL



So simplifies to %28x%5E2-y%5E2%29%2F%28x%5E3%29.


In other words,