bài 1) rút gọn

1) 5√\(\frac{1}{5}\) 2)\(\frac{12}{5}\)√\(\frac{5}{4}\) 3)\(\frac{30}{5\sqrt{6}}\) 4) \(\frac{20}{2\sqrt{5}}\) 5)\(\frac{2-\sqrt{2}}{\sqrt{2}}\) 6) \(\frac{11+\sqrt{11}}{1+\sqrt{ }11}\) 7) \(\frac{\sqrt{21-\sqrt{7}}}{1-\sqrt{3}}\) 8)\(\frac{\sqrt{2+\sqrt{3}}}{2+\sqrt{6}}\) 9)\(\frac{\sqrt{10-\sqrt{2}}}{\sqrt{5-}1}\) 10)\(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt[]{2}}\)

bài 2) với các biểu thức đã cho là có nghĩa và rút gọn

1)\(\frac{x-\sqrt{x}}{\sqrt{x}-1}\) 2)\(\frac{x\sqrt{x}-2x}{2-\sqrt{x}}\) 3) \(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\) 4) \(\frac{a\sqrt{b}-\sqrt{a}}{\sqrt{b}-b\sqrt{a}}\) 5) \(\frac{a-1}{\sqrt{a}+1}\) 6) \(\frac{4-x}{2\sqrt{x}-x}\) 7)\(\frac{a+1+2\sqrt{a}}{1+\sqrt{a}}\) 8)\(\frac{3\sqrt{x}-x}{3+2\sqrt{3x}-x}\) 9)\(\frac{y+12-4\sqrt{3y}}{y-12}\) 10)\(\frac{4\sqrt{x}-x-4}{x-4}\) 11)\(\frac{x+y-2\sqrt{xy}}{x\sqrt{y}-y\sqrt{x}}\)

Rút gọn:

A= (\(\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}-\frac{\sqrt{x}-2}{x-1}\)). \(\frac{\sqrt{x}+1}{\sqrt{x}}\)với x>0 và x\(\ne1\)

B= (\(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\)) : \(\frac{\sqrt{x}+1}{x^2-x}\)với x>0 và x\(\ne1\)

C= ( \(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\)) : \(\frac{1}{\sqrt{a}.\left(\sqrt{a}-1\right)}\)với a>0 và a \(\ne1\)

D= (\(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}\)) : \(\frac{2.\left(x-2\sqrt{x}+1\right)}{x-1}\)với x>0 và x\(\ne1\)

1. Rút gọn các biểu thức sau : 

a) P = \(\sqrt{4}-\sqrt{3}\)

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

c) M= \(\sqrt{50}-\sqrt{2}\)

d) N= (\(\frac{1}{\sqrt{x}+2}+\frac{1}{\sqrt{x}-2}\))   : \(\frac{1}{x-4}\)
e) B = ( \(\sqrt{3}-1\))  . \(\frac{3-\sqrt{3}}{2\sqrt{3}}\)

f) C= ( \(\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\)) (\(1-\frac{2}{\sqrt{x}}\)) 

g) E= \(\frac{1}{2-\sqrt{3}}-\frac{1}{2+\sqrt{3}}\)

h) ( \(1+\frac{\sqrt{x}+2}{\sqrt{x}-2}_{ }\)) \(\frac{1}{\sqrt{x}}\)

A = (\(\sqrt{x}-\frac{x+2}{x-1}\)) : ( \(\frac{\sqrt{x}}{\sqrt{x}+1}\)- \(\frac{\sqrt{x}-4}{1-x}\))

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

C=(\(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\)) .(\(\frac{1-x}{\sqrt{2}}\))²

Mọi ng giúp em nhanh với ạ, em cảm ơn ạ.

Rút Gọn 

a)  A \(=\)\(\frac{1}{\sqrt{x}+\sqrt{x-1}}\)\(-\)\(\frac{1}{\sqrt{x}-\sqrt{x-1}}\)\(-\)\(\frac{x\sqrt{x}-x}{1-\sqrt{x}}\)( Rút gọn và Tìm x để A > 0 )

b) B \(=\)\(\left(2-\frac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\)\(\left(2-\frac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)\)

c) C \(=\)\(\left(\frac{x-\sqrt{x}}{\sqrt{x}-1}+2\right)\)\(\left(2-\frac{\sqrt{x}+x}{1+\sqrt{x}}\right)\)

\(\sqrt{x-2\sqrt{x-1}}\)

\(\sqrt{x-1-2\sqrt{x-2}}\)

\(\frac{x}{x^2-4}+\sqrt{x-2}\)

\(\frac{\sqrt{x+2}}{x^2-4}\)

\(\frac{\sqrt{x-1}}{x^2-x}\)

\(\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)

\(\sqrt{x-y}-\sqrt{\frac{1}{y-2}}\)

Tìm ĐK để biểu thức có nghĩa

Rút gọn

\(\frac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}\) -( \(\sqrt{x}-\sqrt{y}\))²

\(\sqrt{\frac{x-2\sqrt{x}}{x+2\sqrt{x}+1}}\) (x >_ 0)
\(\frac{x-1}{\sqrt{y}-1}\) . \(\sqrt{\frac{\left(2\sqrt{y}+1\right)^2}{\left(x-1\right)}}\) với x # 1, y# 1,y>0
\(\sqrt{\frac{\sqrt{a}-1}{\sqrt{b}+1}}\) : \(\sqrt{\frac{\sqrt{b}-1}{\sqrt{a}+1}}\) rồi tính giá trị với a= 7,25 b= 3,25
4x - \(\sqrt{8}\) + \(\sqrt{\frac{x^3+2x^2}{\sqrt{x+2}}}\) với x =- \(\sqrt{2}\)

A = \(\frac{x-4\sqrt{x}+2}{\sqrt{x}-2}\) (\(x\ge0;x\ne4\))

B = \(\frac{x\sqrt{x}-1}{x-1}\) (\(x\ge0;x\ne1\))

C = \(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}+\frac{x+1}{\sqrt{x}}\) ( \(x>0;x\ne1\))

D = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\) (\(x\ge2\))

E = \(\frac{x+\sqrt{x^2-2x}}{x-\sqrt{x^2}-2x}-\frac{x-\sqrt{x^2-2x}}{x+\sqrt{x^2}-2x}\)