Question

Which of the following is the simplified form of y^2-y-12/y^2-9 ?

Answer 1

(y^2-y-12)/(y^2-9)
let us expand them using our idea in diff of two squares and quadratics
(y^2-4y+3y-12)/(y-3)(y+3)
let us do some factorisation here
factor y and 3 out of the first expression respectively
{y(y-4)+3(y-4)}/(y-3)(y+3)
now we get
(y+3)(y-4)/(y-3)(y+3)
there is a cancellation of (y+3)
and the final answer is
(y-4)/(y-3)