Question

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

Answer 1

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

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

Answer 2

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

\(=\dfrac{x}{\left(x-2\right)\left(x+2\right)}+\dfrac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{\left(x+2\right)\left(x-2\right)}\)

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

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