Question

Cho A = ( 2/ 2+x - 4/x^2+4x+4) : ( 2/x^2-4 + 1/ 2-x)       rút gọn a

Answer 1

\(ĐKXĐ:\)\(x\ne\pm2\);   \(x\ne0\)

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

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

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

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

\(=\frac{4-2x}{x+2}\)