$解:原式=\frac{x+1}{(x+1)(x-1)}+\frac{x^2-3x}{(x+1)(x-1)}$
$\hspace{1.4cm}=\frac {x+1+x^2-3x}{(x+1)(x-1)}$
$\hspace{1.4cm}=\frac {x^2-2x+1}{(x+1)(x-1)}$
$\hspace{1.4cm}=\frac{(x-1)^2}{(x+1)(x-1)}$
$\hspace{1.4cm}=\frac{x-1}{x+1}.$
$把x=2代入,得原式=\frac{2-1}{2+1}=\frac{1}{3}.$