Question

Answer 1

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

vậy rút gọn bt A ta được : \(\dfrac{x+2}{x}\)

Answer 2

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