SOLUTION: please help with step by step 5x^2-125 over x^3+5x^2 multiply 6x^2+2x over 5x-25

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Question 200969: please help with step by step 5x^2-125 over x^3+5x^2 multiply 6x^2+2x over 5x-25
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%285x%5E2-125%29%2F%28x%5E3%2B5x%5E2%29%29%28%286x%5E2%2B2x%29%2F%285x-25%29%29 Start with the given expression.


Factor 5x%5E2-125 to get 5%28x-5%29%28x%2B5%29.


Factor x%5E3%2B5x%5E2 to get x%2Ax%28x%2B5%29.


Factor 6x%5E2%2B2x to get 2x%283x%2B1%29.


Factor 5x-25 to get 5%28x-5%29.


%285%2A2x%2A%28x-5%29%28x%2B5%29%283x%2B1%29%29%2F%285x%2Ax%28x%2B5%29%28x-5%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%282%283x%2B1%29%29%2Fx Simplify.


%286x%2B2%29%2Fx Distribute


So %28%285x%5E2-125%29%2F%28x%5E3%2B5x%5E2%29%29%28%286x%5E2%2B2x%29%2F%285x-25%29%29 simplifies to %286x%2B2%29%2Fx.


In other words,