\(\dfrac{x+1}{x-3}\) + \(\dfrac{x-1}{x+3}\) - \(\dfrac{2x-2x^2}{9-x^2}\)
= \(\dfrac{x+1}{x-3}\)+ \(\dfrac{x-1}{x+3}\) + \(\dfrac{2x-2x^2}{x^2-9}\)
= \(\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\) + \(\dfrac{\left(x-1\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}\) + \(\dfrac{2x-2x^2}{\left(x-3\right)\left(x+3\right)}\)
= \(\dfrac{\left(x+1\right)\left(x+3\right)+\left(x-1\right)\left(x-3\right)+2x-2x^2}{\left(x-3\right)\left(x+3\right)}\)
= \(\dfrac{x^2+3x+x+3+\left(x^2-3x-x+3\right)+2x-2x^2}{\left(x-3\right)\left(x+3\right)}\)
= \(\dfrac{x^2+4x+3+x^2-3x-x+3+2x-2x^2}{\left(x-3\right)\left(x+3\right)}\)
= \(\dfrac{6}{\left(x-3\right)\left(x+3\right)}\)
