Question

Rút gọn biểu thức: 

\(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\frac{1}{2-\sqrt{3}}\)

 

Answer 1

\(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\frac{1}{2-\sqrt{3}}\)

\(=\frac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}-\frac{\left(2+\sqrt{3}\right)}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)

\(=\sqrt{3}-2-\sqrt{2}=-2\)

Answer 2

dòng cuối là \(\sqrt{3}-2-\sqrt{3}=-2\)nhá

Answer 3

         Bài làm :

Ta có :

\(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\frac{1}{2-\sqrt{3}}\)

\(=\frac{\sqrt{3}\left(\sqrt{5}-\sqrt{4}\right)}{\sqrt{5}-2}-\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)

\(=\frac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}-\frac{2+\sqrt{3}}{4-3}\)

\(=\sqrt{3}-\left(2+\sqrt{3}\right)\)

\(=\sqrt{3}-2-\sqrt{3}\)

\(=-2\)