Question

Rút gọn:

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

Answer 1

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

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

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

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

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

\(=\frac{x}{x-1}\)