Rút gọn biểu thức A= \(\frac{\sqrt{x}+1}{x-1}-\frac{x+2}{x\sqrt{x}-1}-\frac{\sqrt{x}+1}{x+\sqrt{x}+1}\)

rút gọn A = \(\frac{\sqrt{a}\left(1-a\right)^2}{1+a}:\left[\left(\frac{1-\sqrt{a^3}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1+\sqrt{a^3}}{1+\sqrt{a}}-\sqrt{a}\right)\right]\)

rút gọn A = \(1:\left(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\right)\)

Tính

a/\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)

b/\(\left(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\right)\)

c/\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)

d/\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)

Tính

A/\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)

B/ \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)

C/ \(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)

D/ \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)

tính

a/ (\(\sqrt{2006}\)- \(\sqrt{2005}\)).(\(\sqrt{2006}\)+ \(\sqrt{2005}\))

b/ (\(\frac{1}{7-4\sqrt{3}}\)+ \(\frac{2}{7+4\sqrt{3}}\)).(21+4\(\sqrt{3}\))

c/ \(3\sqrt{\frac{9}{8}}\)- \(\sqrt{\frac{49}{2}}\)+ \(\sqrt{\frac{25}{18}}\)

d/ ( \(5\sqrt{28}-2\sqrt{63}+3\sqrt{112}\)) : \(\sqrt{7}\)

e/ \(\left(\sqrt{5}+\sqrt{3}\right)\sqrt{8-2\sqrt{15}}\)

f/ (\(\frac{4\sqrt{21}-4\sqrt{15}-\sqrt{14}+\sqrt{10}}{4\sqrt{6}-2+4\sqrt{15}-\sqrt{10}}\)

tính

a/ (\(\sqrt{2006}\)- \(\sqrt{2005}\)).(\(\sqrt{2006}\)+ \(\sqrt{2005}\))

b/ (\(\frac{1}{7-4\sqrt{3}}\)+ \(\frac{2}{7+4\sqrt{3}}\)).(21+4\(\sqrt{3}\))

c/ \(3\sqrt{\frac{9}{8}}\)- \(\sqrt{\frac{49}{2}}\)+ \(\sqrt{\frac{25}{18}}\)

d/ ( \(5\sqrt{28}-2\sqrt{63}+3\sqrt{112}\)) : \(\sqrt{7}\)

e/ \(\left(\sqrt{5}+\sqrt{3}\right)\sqrt{8-2\sqrt{15}}\)

f/ (\(\frac{4\sqrt{21}-4\sqrt{15}-\sqrt{14}+\sqrt{10}}{4\sqrt{6}-2+4\sqrt{15}-\sqrt{10}}\)

Tính

a/ \(\sqrt{45}\).\(\sqrt{15}\).\(\sqrt{27}\)

b/\(\frac{\sqrt{27}}{\sqrt{12}}\)+ \(\frac{1}{2}\)

c/\(\sqrt{\frac{1}{3}}\): \(\sqrt{\frac{27}{50}}\). \(\sqrt{2}\)

d/ \(\sqrt{117^2-108^2}\)

Tính

a/ A=\(\sqrt{6-2\sqrt{5}}\) - \(\sqrt{5}\)

b/ B=\(\sqrt{17\sqrt{2}-24}\)+ 4

c/ C=\(\sqrt{12+6\sqrt{3}-4}\)- \(\sqrt{3}\)