Question

Cho P=(\(\dfrac{2+x}{2-x}\)-\(\dfrac{4x^2}{x^2-4}\)-\(\dfrac{2-x}{2+x}\)) : \(\dfrac{x^2-3x}{2x^2-x^3}\)

a.Rút gọn

b.Tìm giá trị của P biết |x-5|=2

c.Tìm x ∈ Z để A ⋮ 4

Answer 1

a) Ta có: \(P=\left(\dfrac{2+x}{2-x}-\dfrac{4x^2}{x^2-4}-\dfrac{2-x}{2+x}\right):\dfrac{x^2-3x}{2x^2-x^3}\)

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

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

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

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

\(=\dfrac{4x^2}{x-3}\)