Question

Perform the indicated operations and simplify.
y-4/y-9 - y+1/y+9 + y-99/y^2-81

Answer 1

common denominator: (y+9)*(y-9)
I think this is what you meant.
(y-4)(y+9) -(y+1)(y-9) -(y-9) all that over the denominator.

y^2+5y-36 -y^2+8y+9 -y+9 over the denominator.

12y -27 over the denominator

3(4y-9) over the denominator.

Answer 2

I have made a guess and put on the minimum parentheses for the problem to make sense. Do not forget to enclose numerators and denominators with parentheses when transcribing expressions from a book or other sources.

(y-4)/(y-9) - (y+1)/(y+9) + (y-99)/(y^2-81)
using (y-9)(y+9)=y²-81
=(y-4)/(y-9) - (y+1)/(y+9) + (y-99)/((y+9)(y-9))
=((y-4)(y+9)-(y+1)(y-9)+(y-99))/((y+9)(y-9))
=(y²+5y-36 - (y²-8y-9) + (y-99))/((y+9)(y-9))
=(14y-126)/((y+9)(y-9))
=14(y-9)/((y+9)(y-9))
=14/(y+9)