Question

Tìm x(x ϵ Z) để A có giá trị nguyên:

\(\left(\dfrac{2+x}{2-x}-\dfrac{4x^2}{x^2-4}-\dfrac{2-x}{2+x}\right):\dfrac{4x^2-12x}{2x^2-x^3}\)

Answer 1

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

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

\(=\dfrac{-4x^2-8x}{x+2}\cdot\dfrac{-x}{4\left(x-3\right)}=\dfrac{-4x\left(x+2\right)}{\left(x+2\right)}\cdot\dfrac{-x}{4\left(x-3\right)}\)

\(=\dfrac{x^2}{x-3}\)