Question

Rút​ gọn P : P= [x/(x+2)(x-2) + 1/x+2 - 2/x-2 ] : ( 1- x/x+2 )

Answer 1

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

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

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

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

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

\(P=\frac{-3}{x-2}.\)