SOLUTION: Write the rational expression x(x+1)^2(x-5)/x(x+2)(x-5)^3 in simplest terms. Show your work.

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Write the rational expression x(x+1)^2(x-5)/x(x+2)(x-5)^3 in simplest terms. Show your work.      Log On

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Question 193271: Write the rational expression x(x+1)^2(x-5)/x(x+2)(x-5)^3 in simplest terms. Show your work.
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%28x%2B1%29%5E2%28x-5%29%29%2F%28x%28x%2B2%29%28x-5%29%5E3%29 Start with the given expression.


%28x%28x%2B1%29%5E2%28x-5%29%29%2F%28x%28x%2B2%29%28x-5%29%28x-5%29%5E2%29 Factor %28x-5%29%5E3 to get %28x-5%29%28x-5%29%5E2


%28highlight%28x%29%28x%2B1%29%5E2%2Ahighlight%28%28x-5%29%29%29%2F%28highlight%28x%29%28x%2B2%29highlight%28%28x-5%29%29%28x-5%29%5E2%29 Highlight the common terms.


%28cross%28x%29%28x%2B1%29%5E2%2Across%28%28x-5%29%29%29%2F%28cross%28x%29%28x%2B2%29cross%28%28x-5%29%29%28x-5%29%5E2%29 Cancel out the common terms.


%28%28x%2B1%29%5E2%29%2F%28%28x%2B2%29%28x-5%29%5E2%29 Simplify


So %28x%28x%2B1%29%5E2%28x-5%29%29%2F%28x%28x%2B2%29%28x-5%29%5E3%29=%28%28x%2B1%29%5E2%29%2F%28%28x%2B2%29%28x-5%29%5E2%29 where x%3C%3E-2, x%3C%3E0, or x%3C%3E5