Question

Rút gọn : \(\left(\frac{x}{x^2-4}+\frac{2}{2-x}+\frac{1}{x+2}\right):\left(x-2-\frac{x^2-10}{x+2}\right)\)

 

Answer 1

\(\left(\frac{x}{x^2-4}+\frac{2}{2-x}+\frac{1}{x+2}\right):\left(x-2-\frac{x^2-10}{x+2}\right)\left(ĐK:x\ne\pm2\right)\)

\(=\frac{x-2\left(x+2\right)+x-2}{\left(x-2\right)\left(x+2\right)}:\frac{\left(x-2\right)\left(x+2\right)-\left(x^2-10\right)}{x+2}\)

\(=\frac{x-2x-4+x-2}{\left(x-2\right)\left(x+2\right)}\cdot\frac{x+2}{x^2-4-x^2+10}\)

\(=\frac{-6\left(x+2\right)}{6\left(x-2\right)\left(x+2\right)}=-\frac{1}{x-2}=\frac{1}{2-x}\)