Question

Cho A= (x(1-x²)² / 1 + x²) : { [(1-x³ / 1-x )+ x].[1+x³ / 1+x] - x}

Rút gọn A

Answer 1

\(A=\left(\dfrac{x\left(1-x^2\right)^2}{1+x^2}\right):\left[\left(\dfrac{1-x^3}{1-x}+x\right)\cdot\left[\dfrac{1+x^3}{1+x}-x\right]\right]\)

\(=\dfrac{x\left(x-1\right)^2\cdot\left(x+1\right)^2}{x^2+1}:\left[\left(x^2+2x+1\right)\cdot\left(x^2-2x+1\right)\right]\)

\(=\dfrac{x\left(x-1\right)^2\cdot\left(x+1\right)^2}{x^2+1}\cdot\dfrac{1}{\left(x-1\right)^2\cdot\left(x+1\right)^2}=\dfrac{x}{x^2+1}\)