Question

Answer 1

a: \(A=\left(\frac{1}{x-1}-\frac{x}{1-x^3}\cdot\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)

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

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

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

b: Khi x=1/2 thì \(A=\left(\frac12+1\right):\left(\frac12-1\right)=\frac32:\frac{-1}{2}=-3\)