SOLUTION: Perform the indicated operations and simplify. {{{(y-2)/(y-9) - (y+1)/(y+9) + (y-135)/(y^2-81)}}} I got {{{41/18}}} as an answer but do not think this is correct.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Perform the indicated operations and simplify. {{{(y-2)/(y-9) - (y+1)/(y+9) + (y-135)/(y^2-81)}}} I got {{{41/18}}} as an answer but do not think this is correct.      Log On


   

Question 197366: Perform the indicated operations and simplify.
%28y-2%29%2F%28y-9%29+-+%28y%2B1%29%2F%28y%2B9%29+%2B+%28y-135%29%2F%28y%5E2-81%29
I got 41%2F18 as an answer but do not think this is correct.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28y-2%29%2F%28y-9%29+-+%28y%2B1%29%2F%28y%2B9%29+%2B+%28y-135%29%2F%28y%5E2-81%29 Start with the given expression.


Factor the last denominator.


Take note that the LCD is %28y-9%29%28y%2B9%29. In order to add/subtract these fractions, we need to get EVERY denominator equal to the LCD.



Multiply the first fraction by %28y%2B9%29%2F%28y%2B9%29


FOIL


Multiply the second fraction by %28y-9%29%2F%28y-9%29


FOIL


Now that every denominator is equal, we can add/subtract the fractions.


%28%28y%5E2%2B7y-18%29-+%28y%5E2-8y-9%29%2B+%28y-135%29%29%2F%28%28y-9%29%28y%2B9%29%29 Combine the fractions.


%28y%5E2%2B7y-18-+y%5E2%2B8y%2B9%2B+y-135%29%2F%28%28y-9%29%28y%2B9%29%29 Distribute


%2816y-144%29%2F%28%28y-9%29%28y%2B9%29%29 Combine like terms.


%2816%28y-9%29%29%2F%28%28y-9%29%28y%2B9%29%29 Factor


%2816%2Ahighlight%28%28y-9%29%29%29%2F%28highlight%28%28y-9%29%29%28y%2B9%29%29 Highlight the common terms.


%2816%2Across%28%28y-9%29%29%29%2F%28cross%28%28y-9%29%29%28y%2B9%29%29 Cancel out the common terms.


16%2F%28y%2B9%29 Simplify.



So %28y-2%29%2F%28y-9%29+-+%28y%2B1%29%2F%28y%2B9%29+%2B+%28y-135%29%2F%28y%5E2-81%29 simplifies to 16%2F%28y%2B9%29


In other words,