Question

How do you simplify `(r-3)/(r^2+6r+9)-(r-9)/(r^2-9)`?

Answer 1

`= 36/((r+3)^2(r-3))`

Explanation:

`(r-3)/(r^2+6r+9) - (r-9)/(r^2-9) =`

`(r-3)/(r+3)^2 - (r-9)/((r-3)(r+3)) =`

`((r-3)^2 - (r-9)(r+3))/((r+3)^2(r-3)) =`

`(cancel(r^2)- cancel(6r)+9 - cancel(r^2)+cancel(6r)+27)/((r+3)^2(r-3))`

`= 36/((r+3)^2(r-3))` [Ans]