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A=\(\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\)
a, Rút gọn biểu thức
b, Cho \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=6\)Tìm Max A
cho biểu thức: Pleft(frac{sqrt{x}+1}{sqrt{xy}+1}+frac{sqrt{xy}+sqrt{x}}{1-sqrt{xy}}+1right):left(1-frac{sqrt{xy}+sqrt{x}}{sqrt{xy}-1}-frac{sqrt{x}+1}{sqrt{xy}+1}right) Pleft(frac{sqrt{x}+1}{sqrt{xy}+1}+frac{sqrt{xy}+sqrt{x}}{1-sqrt{xy}}+1right):left(1-frac{sqrt{xy}+1}{sqrt{xy}-1}-frac{sqrt{x}+1}{sqrt{xy}+1}right).backslash với x,yge0;x,yne1 a) Rút gọn Pb) Tính P khi xsqrt[3]{4-2sqrt{6}}+sqrt[3]{4+2sqrt{6}}và yx^2+6
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cho biểu thức: \(P=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\) \(P=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+1}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right).\backslash\ \)với \(x,y\ge0;x,y\ne1\)
a) Rút gọn P
b) Tính P khi \(x=\sqrt[3]{4-2\sqrt{6}}+\sqrt[3]{4+2\sqrt{6}}\)và \(y=x^2+6\)
Cho \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=6\) Tìm GTLN của \(A=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+\sqrt{1}}{1+\sqrt{xy}}\right)\)
Cho biểu thức : \(A=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\).
a) Rút gọn A .
b) Cho \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=6\). Tính giá trị lớn nhất của A .
Rút gọn\(A=\left(\frac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}+\frac{\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}\right):\left(1+\frac{x+y+2xy}{1-xy}\right)\)
Rút gọn:
\(A=\frac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left[\left(\frac{1}{x}+\frac{1}{y}\right).\frac{1}{x+y+2\sqrt{xy}}+\frac{2}{\left(\sqrt{x}+\sqrt{y}\right)^3}.\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right)\right]\)
\(x=\sqrt{2-\sqrt{3}};y=\sqrt{2+\sqrt{3}}\)
Rút gọn biểu thức A:
\(A=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\)với \(x>0,\)\(y>0,\)\(xy\ne1\)
rút gọn biểu thức:
\(A=\frac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left[\left(\frac{1}{x}+\frac{1}{y}\right).\frac{1}{x+y+2\sqrt{xy}}+\frac{2}{\left(\sqrt{x}+\sqrt{y}\right)^3}.\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right)\right]\)
Rút gọn:a/ frac{left(sqrt{x^2+9}-3right)left(sqrt{x^2+9}+3right)left(x+sqrt{xy}+yright)sqrt{x-2sqrt{xy}+y}}{xleft(xsqrt{x}-ysqrt{y}right)} (với x0, yge0, xney b/ left[left(frac{1}{sqrt{x}}+frac{1}{sqrt{y}}right).frac{2}{sqrt{x}+sqrt{y}}+frac{1}{sqrt{x}}+frac{1}{sqrt{y}}right]:frac{sqrt{x^3}+ysqrt{x}+xsqrt{y}+sqrt{y^3}}{sqrt{x^3y}+sqrt{xy^3}}(với x0 và xne1 c/ left(frac{sqrt{x}+1}{sqrt{xy}+1}+frac{sqrt{xy}+sqrt{x}}{1-sqrt{xy}}+1right):left(1-frac{sqrt{xy}+sqrt{x}}{sqrt{xy}-1}-frac{sqrt{x}+1}{sqrt...
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Rút gọn:
a/ \(\frac{\left(\sqrt{x^2+9}-3\right)\left(\sqrt{x^2+9}+3\right)\left(x+\sqrt{xy}+y\right)\sqrt{x-2\sqrt{xy}+y}}{x\left(x\sqrt{x}-y\sqrt{y}\right)}\) (với x>0, y\(\ge\)0, x\(\ne\)y
b/ \(\left[\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right).\frac{2}{\sqrt{x}+\sqrt{y}}+\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right]:\frac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{x^3y}+\sqrt{xy^3}}\)(với x>0 và x\(\ne\)1
c/ \(\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\)(với x>0 và x\(\ne\)1