( \(\frac{x+1}{2x-2}\)+\(\frac{3}{x^2-1}-\frac{x-3}{2x+2}\) ) . \(\frac{4x^2-4}{5}\)
= ( \(\frac{x+1}{2\left(x-1\right)}+\frac{3}{\left(x+1\right)\left(x-1\right)}-\frac{x+3}{2\left(x+1\right)}\) ) . \(\frac{4\left(x^2-1\right)}{5}\)
= ( \(\frac{\left(x+1\right)^2}{2\left(x+1\right)\left(x-1\right)}+\frac{6}{2\left(x+1\right)\left(x-1\right)}+\frac{-x^2+4x-3}{2\left(x+1\right)\left(x-1\right)}\) ) . \(\frac{4\left(x+1\right)\left(x-1\right)}{5}\)
= \(\frac{x^2+2x+1+6-x^2+4x-3}{2\left(x+1\right)\left(x-1\right)}.\frac{4\left(x+1\right)\left(x-1\right)}{5}\)
= \(\frac{6x+4}{2\left(x+1\right)\left(x-1\right)}.\frac{4\left(x+1\right)\left(x-1\right)}{5}\)
= \(\frac{2\left(3x+2\right)}{2\left(x+1\right)\left(x-1\right)}.\frac{4\left(x+1\right)\left(x-1\right)}{5}\)
= \(\frac{4\left(3x+2\right)}{5}\)
