Question

Rút gọn:

Answer 1

`A=(1/(x-2)-(2x)/(4-x^2)+1/(2+x)).(2/x-1)`

`đkxđ:x ne 0,+-2`

`A=((x+2+2x+x-2)/(x^2-4)).(2-x)/x`

`=(4x)/(x^2-4).(2-x)/x`

`=-4/(x+2)`

Answer 2

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

A=\(\left(\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}+\dfrac{2x}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{\left(x+2\right)\left(x-2\right)}\right).\left(\dfrac{2}{x}-1\right)\)

A=\(\dfrac{4x}{\left(x-2\right)\left(x+2\right)}\).\(\dfrac{2-x}{x}\)

A=\(\dfrac{-4}{x+2}\)

Answer 3

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

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

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

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

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