Question

tính :

\(\dfrac{-x^2}{x-1}\) + \(\dfrac{x^3-x}{x^3+1}\).( \(\dfrac{x}{x^2-2x-1}\) - \(\dfrac{1}{x^2-1}\))

giúp mk với mk cần gấp, cảm ơn trước nha

Answer 1

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

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

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

\(=\dfrac{-x^2}{x-1}+\dfrac{x\left(x^2+1\right)}{x^3+1}\)

\(=\dfrac{-x^5-x^2+\left(x^2-x\right)\left(x^2+1\right)}{\left(x^3+1\right)\left(x-1\right)}\)

\(=\dfrac{-x^5-x^2+x^4+x^2-x^3-x}{\left(x-1\right)\left(x+1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{-x^5+x^4-x^3-x}{\left(x-1\right)\left(x+1\right)\left(x^2-x+1\right)}\)