SOLUTION: Simplify the following expression. (x^(2)-4)/(x^(2)-7x+10)/(x^(2)+6x+5)/(x^(2)-25)

Algebra ->  Rational-functions -> SOLUTION: Simplify the following expression. (x^(2)-4)/(x^(2)-7x+10)/(x^(2)+6x+5)/(x^(2)-25)      Log On


   

Question 325270: Simplify the following expression.
(x^(2)-4)/(x^(2)-7x+10)/(x^(2)+6x+5)/(x^(2)-25)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-4%29%2F%28x%5E2-7x%2B10%29%29%2F%28%28x%5E2%2B6x%2B5%29%2F%28x%5E2-25%29%29 Start with the given expression.


%28%28x%5E2-4%29%2F%28x%5E2-7x%2B10%29%29%28%28x%5E2-25%29%2F%28x%5E2%2B6x%2B5%29%29 Multiply the first fraction %28x%5E2-4%29%2F%28x%5E2-7x%2B10%29 by the reciprocal of the second fraction %28x%5E2%2B6x%2B5%29%2F%28x%5E2-25%29.


Factor x%5E2-4 to get %28x-2%29%28x%2B2%29.


Factor x%5E2-7x%2B10 to get %28x-2%29%28x-5%29.


Factor x%5E2-25 to get %28x-5%29%28x%2B5%29.


Factor x%5E2%2B6x%2B5 to get %28x%2B5%29%28x%2B1%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28x%2B2%29%2F%28x%2B1%29 Simplify.


So %28%28x%5E2-4%29%2F%28x%5E2-7x%2B10%29%29%2F%28%28x%5E2%2B6x%2B5%29%2F%28x%5E2-25%29%29 simplifies to %28x%2B2%29%2F%28x%2B1%29.


In other words,