SOLUTION: I am not sure on how to do this problem???? Could you please help??? Multiply and simplify y^2-81 * y^2-9y ------- ------ y^2 y^2+y-90 Thank you !!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am not sure on how to do this problem???? Could you please help??? Multiply and simplify y^2-81 * y^2-9y ------- ------ y^2 y^2+y-90 Thank you !!      Log On


   

Question 195632: I am not sure on how to do this problem???? Could you please help???
Multiply and simplify
y^2-81 * y^2-9y
------- ------
y^2 y^2+y-90
Thank you !!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28y%5E2-81%29%2F%28y%5E2%29%29%28%28y%5E2-9y%29%2F%28y%5E2%2By-90%29%29 Start with the given expression.


%28%28%28y-9%29%28y%2B9%29%29%2F%28y%5E2%29%29%28%28y%5E2-9y%29%2F%28y%5E2%2By-90%29%29 Factor y%5E2-81 to get %28y-9%29%28y%2B9%29.


%28%28%28y-9%29%28y%2B9%29%29%2F%28y%2Ay%29%29%28%28y%5E2-9y%29%2F%28y%5E2%2By-90%29%29 Factor y%5E2 to get y%2Ay.


%28%28%28y-9%29%28y%2B9%29%29%2F%28y%2Ay%29%29%28%28y%28y-9%29%29%2F%28y%5E2%2By-90%29%29 Factor y%5E2-9y to get y%28y-9%29.


Factor y%5E2%2By-90 to get %28y%2B10%29%28y-9%29.


%28y%28y-9%29%28y%2B9%29%28y-9%29%29%2F%28y%2Ay%28y%2B10%29%28y-9%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28%28y%2B9%29%28y-9%29%29%2F%28y%28y%2B10%29%29 Simplify.


%28y%5E2-81%29%2F%28y%28y%2B10%29%29 FOIL


%28y%5E2-81%29%2F%28y%5E2%2B10y%29 Distribute


So %28%28y%5E2-81%29%2F%28y%5E2%29%29%28%28y%5E2-9y%29%2F%28y%5E2%2By-90%29%29 simplifies to %28y%5E2-81%29%2F%28y%5E2%2B10y%29.


In other words, where y%3C%3E-10, y%3C%3E0, or y%3C%3E9.