Question

Rút gọn :  \(\left(\frac{1}{1-x}+\frac{1}{1+x}\right)\div\left(\frac{1}{1-x}-\frac{1}{1+x}\right)-\frac{3}{2x}\)

Answer 1

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

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

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

\(=\dfrac{1}{x}-\dfrac{3}{2x}=\dfrac{2-3}{2x}=\dfrac{-1}{2x}\)