Question

Answer 1

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

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

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

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

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