Question

Rút gọn A

A=\(\left(\frac{2}{x+2}-\frac{4}{x^2+4x+4}\right):\left(\frac{2}{x^2-4}+\frac{1}{2-x}\right)\)

GIÚP MÌNH VỚI MAI MINH ĐI HỌC RỒI

Answer 1

\(\text{Đ}K\text{X}\text{Đ}:x\ne\pm2\)

Ta có: \(A=\left(\frac{2}{x+2}-\frac{4}{x^2+4x+4}\right)\div\left(\frac{2}{x^2-4}+\frac{1}{2-x}\right)\)

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

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