Question

Rút gọn:

1. \(\left(\dfrac{1}{2-\sqrt{3}}-\dfrac{3}{\sqrt{7}-2}\right):\dfrac{2}{\sqrt{7}+\sqrt{3}}\)

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

Answer 1

1.

\(=\left[\frac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}-\frac{3(\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)}\right].\frac{\sqrt{7}+\sqrt{3}}{2}\)

\(=\left(\frac{2+\sqrt{3}}{4-3}-\frac{3(\sqrt{7}+2)}{7-4}\right).\frac{\sqrt{7}+\sqrt{3}}{2}\)

\(=(2+\sqrt{3}-\sqrt{7}-2).\frac{\sqrt{7}+\sqrt{3}}{2}=\frac{(\sqrt{3}-\sqrt{7})(\sqrt{7}+\sqrt{3})}{2}=\frac{3-7}{2}=-2\)

 

Answer 2

2. ĐKXĐ: $x>0; x\neq 1$

\(=\left[\frac{-\sqrt{x}(1-\sqrt{x})}{1-\sqrt{x}}-1\right].\sqrt{x}(1-\sqrt{x})+\frac{1}{x}\)

\(=-(\sqrt{x}+1)(1-\sqrt{x})\sqrt{x}+\frac{1}{x}=-(1-x).\sqrt{x}+\frac{1}{x}\)

\(=x\sqrt{x}-\sqrt{x}+\frac{1}{x}\)