Usually, "simplify" means to remove any common factors and express the sum as a single fraction, often in multiplie-out form.
If you factor what you've got, you will write it as
[tex]\dfrac{(m+2)(m-2)}{(m+1)}+\dfrac{(m+2)}{(m+1)^2}=\dfrac{m+2}{m+1}\cdot\left((m-2)+\dfrac{1}{m+1}\right)\\\\=\dfrac{m+2}{m+1}\cdot\dfrac{(m-2)(m+1)+1}{m+1}\\\\=\dfrac{(m+2)(m^2-m-1)}{(m+1)^2}\\\\=\dfrac{m^3+m^2-3m-2}{m^2+2m+1}[/tex]
