Question

rút gọn biểu thức :

1/ \(\frac{6-6\sqrt{3}}{1-\sqrt{3}}+\frac{3\sqrt{3}+3}{\sqrt{3}+1}\)

2/ \(\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}+\frac{3+\sqrt{3}}{\sqrt{3}}\)

3/ \(\frac{2-\sqrt{2}}{1-\sqrt{2}}+\frac{\sqrt{2}-\sqrt{6}}{\sqrt{3}-1}\)

Answer 1

1) \(\frac{6-6\sqrt{3}}{1-\sqrt{3}}+\frac{3\sqrt{3}+3}{\sqrt{3}+1}\)

= \(\frac{6\left(1-\sqrt{3}\right)}{1-\sqrt{3}}+\frac{3\left(\sqrt{3}+1\right)}{\sqrt{3}+1}\)

= 6+3

=9

2) \(\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}+\frac{3+\sqrt{3}}{\sqrt{3}}\)

= \(\frac{-\sqrt{3}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}+\frac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}}\)

= \(-\sqrt{3}+\sqrt{3}+1\)

=1

3)\(\frac{2-\sqrt{2}}{1-\sqrt{2}}+\frac{\sqrt{2}-\sqrt{6}}{\sqrt{3}-1}\)

= \(\frac{-\sqrt{2}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}-\frac{\sqrt{2}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}\)

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