Question

Đã trả lời bởi chuyên gia

Answer 1

\[\begin{array}{l}
a)\frac{{x\sqrt y + y\sqrt x }}{{\sqrt {xy} }}:\frac{1}{{\sqrt x - \sqrt y }} = x - y\;\\
x;y > 0;x \ne y\\
xet:\\
VT = \frac{{x\sqrt y + y\sqrt x }}{{\sqrt {xy} }}:\frac{1}{{\sqrt x - \sqrt y }}\\
= \frac{{\sqrt {xy} \left( {\sqrt x + \sqrt y } \right)}}{{\sqrt {xy} }}.\left( {\sqrt x - \sqrt y } \right)\\
= \left( {\sqrt x + \sqrt y } \right)\left( {\sqrt x - \sqrt y } \right)\\
= x - y = VP\\
Vay:\frac{{x\sqrt y + y\sqrt x }}{{\sqrt {xy} }}:\frac{1}{{\sqrt x - \sqrt y }} = x - y\;\\
b)\frac{{\sqrt y }}{{x - \sqrt {xy} }} + \frac{{\sqrt x }}{{y - \sqrt {xy} }} = \; - \frac{{\sqrt x + \sqrt y }}{{\sqrt {xy} }}\\
x;y > 0;x \ne y\\
xet:\\
VT = \frac{{\sqrt y }}{{x - \sqrt {xy} }} + \frac{{\sqrt x }}{{y - \sqrt {xy} }}\\
= \frac{{\sqrt y }}{{\sqrt x \left( {\sqrt x - \sqrt y } \right)}} + \frac{{\sqrt x }}{{\sqrt y \left( {\sqrt y - \sqrt x } \right)}}\\
= \frac{{\sqrt y .\sqrt y - \sqrt x .\sqrt x }}{{\sqrt x .\sqrt y \left( {\sqrt x - \sqrt y } \right)}}\\
= \frac{{y - x}}{{\sqrt {xy} \left( {\sqrt x - \sqrt y } \right)}}\\
= - \frac{{\left( {\sqrt x - \sqrt y } \right)\left( {\sqrt x + \sqrt y } \right)}}{{\sqrt {xy} \left( {\sqrt x - \sqrt y } \right)}}\\
= - \frac{{\sqrt x + \sqrt y }}{{\sqrt {xy} }} = VP\\
vay:\frac{{\sqrt y }}{{x - \sqrt {xy} }} + \frac{{\sqrt x }}{{y - \sqrt {xy} }} = \; - \frac{{\sqrt x + \sqrt y }}{{\sqrt {xy} }}
\end{array}\]

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Answer 2

\[\begin{array}{l}
a)\frac{{x\sqrt y + y\sqrt x }}{{\sqrt {xy} }}:\frac{1}{{\sqrt x - \sqrt y }} = x - y\;\\
x;y > 0;x \ne y\\
xet:\\
VT = \frac{{x\sqrt y + y\sqrt x }}{{\sqrt {xy} }}:\frac{1}{{\sqrt x - \sqrt y }}\\
= \frac{{\sqrt {xy} \left( {\sqrt x + \sqrt y } \right)}}{{\sqrt {xy} }}.\left( {\sqrt x - \sqrt y } \right)\\
= \left( {\sqrt x + \sqrt y } \right)\left( {\sqrt x - \sqrt y } \right)\\
= x - y = VP\\
Vay:\frac{{x\sqrt y + y\sqrt x }}{{\sqrt {xy} }}:\frac{1}{{\sqrt x - \sqrt y }} = x - y\;\\
b)\frac{{\sqrt y }}{{x - \sqrt {xy} }} + \frac{{\sqrt x }}{{y - \sqrt {xy} }} = \; - \frac{{\sqrt x + \sqrt y }}{{\sqrt {xy} }}\\
x;y > 0;x \ne y\\
xet:\\
VT = \frac{{\sqrt y }}{{x - \sqrt {xy} }} + \frac{{\sqrt x }}{{y - \sqrt {xy} }}\\
= \frac{{\sqrt y }}{{\sqrt x \left( {\sqrt x - \sqrt y } \right)}} + \frac{{\sqrt x }}{{\sqrt y \left( {\sqrt y - \sqrt x } \right)}}\\
= \frac{{\sqrt y .\sqrt y - \sqrt x .\sqrt x }}{{\sqrt x .\sqrt y \left( {\sqrt x - \sqrt y } \right)}}\\
= \frac{{y - x}}{{\sqrt {xy} \left( {\sqrt x - \sqrt y } \right)}}\\
= - \frac{{\left( {\sqrt x - \sqrt y } \right)\left( {\sqrt x + \sqrt y } \right)}}{{\sqrt {xy} \left( {\sqrt x - \sqrt y } \right)}}\\
= - \frac{{\sqrt x + \sqrt y }}{{\sqrt {xy} }} = VP\\
vay:\frac{{\sqrt y }}{{x - \sqrt {xy} }} + \frac{{\sqrt x }}{{y - \sqrt {xy} }} = \; - \frac{{\sqrt x + \sqrt y }}{{\sqrt {xy} }}
\end{array}\]

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