## Precalculus (6th Edition)

$\color{blue}{\dfrac{2m^2+2}{(m-1)(m+1)}}$
The expressions are not similar since they have different denominators. Make the expressions similar using their LCD $(m+1)(m-1)$ to obtain: $=\dfrac{(m+1)\color{red}{(m+1)}}{(m-1)\color{red}{(m+1)}} + \dfrac{(m-1)\color{red}{(m-1)}}{(m+1)\color{red}{(m-1)}} \\=\dfrac{m^2+m+m+1}{(m-1)(m+1)}+\dfrac{m^2-m-m+1}{(m+1)(m-1)} \\=\dfrac{m^2+2m+1}{(m-1)(m+1)}+\dfrac{m^2-2m+1}{(m+1)(m-1)}$ Add the numerators and copy the denominator to obtain: $=\dfrac{(m^2+2m+1)+(m^2-2m+1)}{(m-1)(m+1)} \\=\dfrac{(m^2+m^2)+(2m-2m)+(1+1)}{(m-1)(m+1)} \\=\color{blue}{\dfrac{2m^2+2}{(m-1)(m+1)}}$