Question

Rút gọn \(A=(\dfrac{2+x}{2-x}+\dfrac{2-x}{2+x}-\dfrac{4x^2}{x^2-4}):\dfrac{x^2-6x+9}{6-x^2+x}\)

Answer 1

\(=\dfrac{-\left(x^2+4x+4\right)-\left(x^2-4x+4\right)-4x^2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{-\left(x^2-x-6\right)}{\left(x-3\right)^2}\)

\(=\dfrac{-x^2-4x-4-x^2+4x-4-4x^2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{-\left(x-3\right)\left(x+2\right)}{\left(x-3\right)^2}\)

\(=\dfrac{-6x^2-8}{\left(x-2\right)}\cdot-\dfrac{1}{x-3}\)

\(=\dfrac{6x^2+8}{\left(x-2\right)\left(x-3\right)}\)