Question

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

Answer 1

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

\(=\dfrac{2x}{x-2}+\dfrac{3x}{x+2}-\dfrac{x\left(x+6\right)}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{2x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{3x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{x\left(x+6\right)}{\left(x-2\right)\left(x+2\right)}\)

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

\(=\dfrac{4x^2-8x}{\left(x-2\right)\left(x+2\right)}\)

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

\(=\dfrac{4x}{x+2}\)