SOLUTION: Hi, I am in need of help with this problem.... Simplify y^2-y-2 -------- y^2-6y-7 ___________ ____ y^2+7y+12 ------

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, I am in need of help with this problem.... Simplify y^2-y-2 -------- y^2-6y-7 ___________ ____ y^2+7y+12 ------      Log On


   

Question 196719: Hi, I am in need of help with this problem....
Simplify

y^2-y-2
--------
y^2-6y-7
________________

y^2+7y+12
---------
y^2-4y-21
Thank you for all your help. I really appreciate it!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28y%5E2+-+y-2%29%2F%28y%5E2-6y-7%29%29%2F%28%28y%5E2%2B7y%2B12%29%2F%28y%5E2-4y-21%29%29 Start with the given expression.


%28%28y%5E2-y-2%29%2F%28y%5E2-6y-7%29%29%28%28y%5E2-4y-21%29%2F%28y%5E2%2B7y%2B12%29%29 Multiply the first fraction %28y%5E2-y-2%29%2F%28y%5E2-6y-7%29 by the reciprocal of the second fraction %28y%5E2%2B7y%2B12%29%2F%28y%5E2-4y-21%29.


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


Factor y%5E2-6y-7 to get %28y%2B1%29%28y-7%29.


Factor y%5E2-4y-21 to get %28y%2B3%29%28y-7%29.


Factor y%5E2%2B7y%2B12 to get %28y%2B4%29%28y%2B3%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


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


So %28%28y%5E2+-+y-2%29%2F%28y%5E2-6y-7%29%29%2F%28%28y%5E2%2B7y%2B12%29%2F%28y%5E2-4y-21%29%29 simplifies to %28y-2%29%2F%28y%2B4%29.


In other words, where y%3C%3E-4, y%3C%3E-3, y%3C%3E-1, or y%3C%3E7