Question

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

 

Answer 1

Đk: \(x\ne\pm1\)

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

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

\(=\dfrac{\left(x+1\right)^2+6-\left(x+3\right)\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}.\dfrac{4\left(x-1\right)\left(x+1\right)}{5}\)

\(=\dfrac{10}{2\left(x-1\right)\left(x+1\right)}.\dfrac{4\left(x-1\right)\left(x+1\right)}{5}\)\(=4\)