Question

(\(\dfrac{3x-2}{x-2}\) - \(\dfrac{x}{x+2}\)+ \(\dfrac{4}{x^2-4}\)) : \(\dfrac{x+3}{x^2-4}\)

Answer 1

\(\left(\dfrac{3x-2}{x-2}-\dfrac{x}{x+2}+\dfrac{4}{x^2-4}\right):\dfrac{x+3}{x^2-4}\left(x\ne\pm2;x\ne-3\right)\)

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

\(=\dfrac{3x^2+4x-4-x^2+2x+4}{x^2-4}\cdot\dfrac{x^2-4}{x+3}\)

\(=\dfrac{2x^2+6x}{x+3}\)

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