SOLUTION: y^2-4y-5/y^2+5y+4

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Question 187784This question is from textbook college mathematics 1
: y^2-4y-5/y^2+5y+4 This question is from textbook college mathematics 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28y%5E2-4y-5%29%2F%28y%5E2%2B5y%2B4%29 Start with the given expression.


%28%28y%2B1%29%28y-5%29%29%2F%28y%5E2%2B5y%2B4%29 Factor y%5E2-4y-5 to get %28y%2B1%29%28y-5%29.


%28%28y%2B1%29%28y-5%29%29%2F%28%28y%2B4%29%28y%2B1%29%29 Factor y%5E2%2B5y%2B4 to get %28y%2B4%29%28y%2B1%29.


%28highlight%28%28y%2B1%29%29%28y-5%29%29%2F%28%28y%2B4%29highlight%28%28y%2B1%29%29%29 Highlight the common terms.


%28cross%28%28y%2B1%29%29%28y-5%29%29%2F%28%28y%2B4%29cross%28%28y%2B1%29%29%29 Cancel out the common terms.


%28y-5%29%2F%28y%2B4%29 Simplify.


So %28y%5E2-4y-5%29%2F%28y%5E2%2B5y%2B4%29 simplifies to %28y-5%29%2F%28y%2B4%29.


In other words, %28y%5E2-4y-5%29%2F%28y%5E2%2B5y%2B4%29=%28y-5%29%2F%28y%2B4%29 where y%3C%3E-4 or y%3C%3E-1