Question

Rút gọn biểu thức:

a.\(\left(\dfrac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\dfrac{1}{\sqrt{3}+\sqrt{5}}\)

b. \(\dfrac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}+\dfrac{3+6\sqrt{3}}{\sqrt{3}}-\dfrac{13}{\sqrt{3}+4}\)

c.\(\dfrac{7\sqrt{3}-3\sqrt{7}}{\sqrt{7}-\sqrt{3}}+\dfrac{4}{5-\sqrt{21}}-\dfrac{6\sqrt{7}}{\sqrt{3}}\)

d. \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\) với a \(\ge0\)

e. \(2\sqrt{3a}+\sqrt{75a}+a\sqrt{\dfrac{13,5}{2a}}-\dfrac{2}{5}\sqrt{300a^3}\) với a\(\ge0\)

g. \(\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{x+\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{x+2\sqrt{x}+1}\) với x >0 ; x\(\ne1\)

Answer 1

a: \(=\left(\sqrt{3}-\sqrt{5}\right)\cdot\left(\sqrt{3}+\sqrt{5}\right)=3-5=-2\)

b: \(=-\sqrt{3}+\sqrt{3}+6-4+\sqrt{3}=2+\sqrt{3}\)

c: \(=\sqrt{21}+5+\sqrt{21}-2\sqrt{21}=5\)

d: \(=3\sqrt{a}-4\sqrt{a}+7\sqrt{a}=6\sqrt{a}\)