Rút gọn:
\(A=\left(1+\dfrac{\sqrt{x}}{x+1}\right):\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}\right)-1\)
Rút gọn : A=\(\left(1-\frac{\sqrt{x}}{\sqrt{x}+1}\right):\left(\frac{2+\sqrt{x}}{x-5\sqrt{x}+6}+\frac{3+\sqrt{x}}{\sqrt{x}-2}-\frac{2+\sqrt{x}}{\sqrt{x}-3}\right)\)
Cho A=\(\left(1-\frac{\sqrt{x}}{\sqrt{x}+1}\right):\left(\frac{2+\sqrt{x}}{x-5\sqrt{x}+6}+\frac{3+\sqrt{x}}{\sqrt{x}-2}-\frac{2+\sqrt{x}}{\sqrt{x}-3}\right)\)
Tìm tập xác định và rút gọn A
1. Tìm x:
a/\(\sqrt{\dfrac{x-1}{x-3}=2}\)
b/\(\sqrt{\left(x-2\right)^2=7}\)
2. Tính:
\(\dfrac{\sqrt{6}+\sqrt{10}}{3+\sqrt{15}}\)
1. Chứng minh:\(\left(\frac{x\sqrt{x}+27y\sqrt{y}}{3\sqrt{x}+9\sqrt{y}}-\sqrt{xy}\right).\left(\frac{3\sqrt{x}+9\sqrt{y}}{9y-x}\right)^2>\sqrt{8}\)
2. Rút gọn A= \(\frac{\sqrt{a+2\sqrt{a-1}}+\sqrt{a-2\sqrt{a-1}}}{\sqrt{a+\sqrt{2a-1}}-\sqrt{a-\sqrt{2a-1}}}\)
Tìm x thuộc Z
a, \(\frac{\sqrt{x}-3}{\sqrt{x}+1}\)
b, \(\frac{2\left(\sqrt{2}-5\right)}{\sqrt{x}+1}\in Z\)
c, \(\frac{2\sqrt{x}+1}{3\sqrt{x}-1}\in Z\)
d, \(\frac{\sqrt{x}-2}{\sqrt{x}+2}\in Z\)
Tì giá trị x nguyên để các biểu thức sau nhận giá trị nguyên:
\(A=\frac{3x-5}{2x-1}\)
\(B=\frac{5x+3}{x-3}\)
\(C=\frac{3\left|x\right|+1}{3\left|x\right|-1}\)
\(D=\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(E=\frac{2\sqrt{x}+3}{\sqrt{x}-2}\)
\(F=\frac{\sqrt{x}+1}{\sqrt{x}-3}\)
\(G=\frac{5\sqrt{x}+4}{\sqrt{x-4}}\)
\(H=\frac{\sqrt{x}+7}{\sqrt{x}-3}\)
Rút gọn :
(\(\frac{\sqrt{x}}{\sqrt{x}-1}\) - \(\frac{1}{x-\sqrt{x}}\)) : ( \(\frac{1}{1+\sqrt{x}}\) - \(\frac{2}{1-x}\))
Rút gọn:
\(A=1+\sqrt{x-1}+\sqrt{x-2\sqrt{x-1}}\)
Tìm x biết:
a)\(\left|\sqrt{2}-x\right|=\sqrt{2}\)
b)\(\left|x-1\right|=\sqrt{3}+2\)
c)\(\left|1-2x\right|=\sqrt{5}-1\)
d)\(\left|1-x\right|=\sqrt{2}-0,\left(1\right)\)
e)\(\left|x-\sqrt{3}\right|=\sqrt{3}-1\)
f)\(\left|x-\sqrt{2}\right|=1,\left(4\right)\)