Question

Rút gọn: B=\(\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)

Answer 1

Đặt \(\sqrt{x}=a\)

\(B=\left(\dfrac{1}{a-1}-\dfrac{1}{a}\right):\left(\dfrac{a+1}{a-2}-\dfrac{a+2}{a-1}\right)\)

\(=\left(\dfrac{a-a+1}{\left(a-1\right)a}\right):\left(\dfrac{a^2-1-a^2+2}{\left(a-2\right)\left(a-1\right)}\right)\)

\(=\left(\dfrac{1}{\left(a-1\right)a}\right):\left(\dfrac{1}{\left(a-2\right)\left(a-1\right)}\right)\)

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

\(\Rightarrow B=\dfrac{\sqrt{x}-2}{\sqrt{x}}\)

Vậy...