Question

Rút gọn A

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

Answer 1

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

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

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

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

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

   =\(\dfrac{1}{x-1}\)