SOLUTION: y^2/y-7 x y^2-5y-14/y^2+4y

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Question 151083: y^2/y-7 x y^2-5y-14/y^2+4y
Answer by jim_thompson5910(28503) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28y%5E2%29%2F%28y-7%29%29%28%28y%5E2-5y-14%29%2F%28y%5E2%2B4y%29%29 Start with the given expression.


%28%28y%2Ay%29%2F%28y-7%29%29%28%28y%5E2-5y-14%29%2F%28y%5E2%2B4y%29%29 Factor y%5E2 to get y%2Ay.


%28%28y%2Ay%29%2F%281%28y-7%29%29%29%28%28%28y%2B2%29%2A%28y-7%29%29%2F%28y%5E2%2B4y%29%29 Factor y%5E2-5y-14 to get %28y%2B2%29%28y-7%29.


%28%28y%2Ay%29%2F%28y-7%29%29%28%28%28y%2B2%29%2A%28y-7%29%29%2F%28y%2A%28y%2B4%29%29%29 Factor y%5E2%2B4y to get y%28y%2B4%29.


%28y%2Ay%28y%2B2%29%2A%28y-7%29%29%2F%28y%28y-7%29%28y%2B4%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28y%28y%2B2%29%29%2F%28y%2B4%29 Simplify.


%28y%5E2%2B2y%29%2F%28y%2B4%29 Distribute


So %28%28y%5E2%29%2F%28y-7%29%29%28%28y%5E2-5y-14%29%2F%28y%5E2%2B4y%29%29 simplifies to %28y%5E2%2B2y%29%2F%28y%2B4%29.


In other words, where y%3C%3E0, y%3C%3E-4, or y%3C%3E7