Question

Упростите выражение ______________________

Answer 1

См скриншот
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Answer 2

$\frac{ \sqrt{a}- \sqrt{b} }{a \sqrt{b} +b \sqrt{a} }+ \frac{ \sqrt{a} + \sqrt{b} }{a \sqrt{b}-b \sqrt{a}}= \frac{ \sqrt{a} - \sqrt{b} }{ \sqrt{a}* \sqrt{b}( \sqrt{a} + \sqrt{b}) }+ \frac{ \sqrt{a}+ \sqrt{b}}{ \sqrt{a}* \sqrt{b}( \sqrt{a}- \sqrt{b})}=$$\frac{( \sqrt{a}- \sqrt{b}) ^{2}+( \sqrt{a}+ \sqrt{b}) ^{2} }{ \sqrt{a}* \sqrt{b}( \sqrt{a}+ \sqrt{b} )( \sqrt{a}- \sqrt{b})}= \frac{a-2 \sqrt{ab}+b+a+2 \sqrt{ab}+b}{ \sqrt{a}* \sqrt{b} (a-b) }= \frac{2(a+b)}{ \sqrt{ab}(a-b) }\\\\\\ \frac{2(a+b)}{ \sqrt{ab}(a-b) }* \frac{ \sqrt{a ^{3}b } }{a+b}= \frac{2}{ \sqrt{ab}(a-b) } *a \sqrt{ab}= \frac{2a}{a-b}\\\\\\ \frac{2a}{a-b}- \frac{2b}{a-b}= \frac{2(a-b)}{a-b} =2$