\(\dfrac{1}{x-y}\) + \(\dfrac{2}{x+y}\) + \(\dfrac{3x}{y^2-x^2}\)
= \(\dfrac{x+y+2x-2y}{x^2-y^2}\) - \(\dfrac{3x}{x^2-y^2}\)
= \(\dfrac{-y}{x^2-y^2}\)
\(\dfrac{x+1}{2x-2}\) + \(\dfrac{x^2+3}{2-2x^2}\)
= \(\dfrac{x+1}{2(x-1)}\) - \(\dfrac{x^2+3}{2.(x^2-1)}\)
= \(\dfrac{x^2+2x+1-x^2-3}{2.(x-1)(x+1)}\)
= \(\dfrac{2x-2}{2.(x-1)(x+1)}\)
= \(\dfrac{1}{x+1}\)
\(\dfrac{1}{x+2}\) + \(\dfrac{2}{2-x}\) + \(\dfrac{x}{x^2-4}\)
= \(\dfrac{2-x+2x+4}{(2-x)(x+2)}\) - \(\dfrac{x}{(2-x)(2+x)}\)
= \(\dfrac{6}{(2-x)(2+x)}\)