\(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\dfrac{1}{\sqrt{x}-\sqrt{y}}=x-y\)
\(\Leftrightarrow\dfrac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{xy}}:\dfrac{1}{\sqrt{x}-\sqrt{y}}=x-y\)
\(\Leftrightarrow\left(\sqrt{x}+\sqrt{y}\right).\left(\sqrt{x}-\sqrt{y}\right)=x-y\)
\(\Leftrightarrow x-y=x-y\)
Vậy VT=VP (đpcm)
CM:
\(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{4}}=\dfrac{\sqrt{6}}{6}\)
\(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\dfrac{1}{\sqrt{x}+\sqrt{y}}=x-y\) với x.0, y>0, x≠y
\(\dfrac{\sqrt{y}}{x-\sqrt{xy}}+\dfrac{\sqrt{x}}{y-\sqrt{xy}}=\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{xy}}\)với x>0, y>0, x≠y
Chứng minh : A < 0 với y > x > 0
A = \(\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}+\dfrac{\sqrt{y}}{\sqrt{y}-\sqrt{x}}=\dfrac{2\sqrt{xy}}{x-y}\)
\(\dfrac{\sqrt{y}}{x-\sqrt{ }xy}+\dfrac{\sqrt{x}}{y-\sqrt{ }xy}=-\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{xy}}\)
Chứng minh đẳng thức với x ; y lớn hơn 0 ; x khác y
Chứng minh :
a) \(\dfrac{\left(x\sqrt{y}+y\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}=x-y\) với \(x>0;y>0\)
b) \(\dfrac{\sqrt{x^3}-1}{\sqrt{x}-1}=x+\sqrt{x}+1\) với \(x\ge0;x\ne1\)
tính
\(\dfrac{\sqrt{2}-1}{\sqrt{2}+1}-\dfrac{1}{1+\sqrt{2}}+\dfrac{\sqrt{2}+1}{\sqrt{2}}\)
\(\sqrt{x}-2+\dfrac{10-x}{\sqrt{x}+2}\) với x>=0
\(\dfrac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)
\(\left(\dfrac{2x+1}{\sqrt{x^3-1}}-\dfrac{\sqrt{x}}{x+\sqrt{x+1}}\right)\left(\dfrac{1+\sqrt{x^3}}{1+\sqrt{x}}-\sqrt{x}\right)\)
\(\dfrac{\sqrt{x-2\sqrt{x-1}+}\sqrt{x+2\sqrt{x-1}}}{\sqrt{\dfrac{1}{x^2}-\dfrac{2}{x}+1}}\)
\(\left(\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\sqrt{xy}\right):\left(x-y\right)+\dfrac{2\sqrt{y}}{\sqrt{x}+\sqrt{y}}\)
\(\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{x+9}{9-x}\right):\left(\dfrac{3\sqrt{x}+1}{x-3\sqrt{x}}-\dfrac{1}{\sqrt{x}}\right)\)
Mí bạn giải giúp mik bài này nhé!:))))))))))))))))))))))))))))))ARIGATO MÍ BẠN NHIW!!!!!!!!!!:)))))))))))))))))))))))))))))))))
Rút gọn biểu thức:
C=\(\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}\right)\div\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2}{x-1}\right)vớix\ge0,x\ne1\)
D=\(\left(\sqrt{x}+\dfrac{y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\div\left(\dfrac{x}{\sqrt{xy}+y}+\dfrac{y}{\sqrt{xy}-x}-\dfrac{x+y}{\sqrt{xy}}\right)\)
Lm nhanh giúp mk nhé!
khử mẫu của biểu thức dưới dấu căn bậc hai
a)\(6\sqrt{\dfrac{x}{2y}}\) với \(x< 0,y< 0\)
b)\(\dfrac{4xy^2}{3}\sqrt{\dfrac{9}{xy}}\) với \(x>0,y>0\)
A = 5, xy = \(\dfrac{1}{36}\) . Tìm x,y biết A = \(\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{xy}}\)