\(\dfrac{3}{2x+2}+\dfrac{2-x}{x^2-1}\)
\(=\dfrac{3}{2\left(x+1\right)}+\dfrac{2-x}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{3\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}+\dfrac{2\left(2-x\right)}{2\left(x-1\right)\left(x+1\right)}\)
\(=3\left(x-1\right)+2\left(2-x\right)\)
\(=3x-3+4-2x\)
\(=x+1\)