Question

Rút gọn : \(\left(\frac{1+x}{x}+\frac{1}{4x^2}\right)\left(\frac{1-2x}{1+2x}-\frac{1}{1-4x^2}\times\frac{1-4x+4x^2}{1+2x}\right)-\frac{1}{2x}\)

Answer 1

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

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

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

\(=\dfrac{-4x^2+1+2x-1}{4x^2}-\dfrac{1}{2x}\)

\(=\dfrac{-4x^2+2x}{4x^2}-\dfrac{1}{2x}\)

\(=\dfrac{-2x\left(2x-1\right)}{2x\cdot2x}-\dfrac{1}{2x}\)

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