Simplify by removing factors of 1.

m^2 - 9/(m+3)^2

Do you mean (m^2-9)/(m+3)^2 ?

If so, you should have had parentheses for the numerator.

That can be written
(m+3)(m-3)/[(m+3)(m+3)]
Cancel out the m+3 terms for a simplified version.