Сократите дробь:a) √5+1/√10+√2 б) 2-√2/√6-√3в) x²-2/√2x+2. Created by harton228. algebra-ru

√2x+2...

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Сократите дробь:
a) √5+1/√10+√2

б) 2-√2/√6-√3

в) x²-2/√2x+2

Answers & Comments

АннаАрт A)
$\frac{\sqrt{5}+1}{\sqrt{10}+\sqrt{2}}=\frac{\sqrt{2}(\sqrt{5}+1)}{\sqrt{2}(\sqrt{10}+\sqrt{2})}=\frac{\sqrt{10}+\sqrt{2}}{\sqrt{2}(\sqrt{10}+\sqrt{2})}=\frac{1}{\sqrt{2}}$

б)
$\frac{2-\sqrt{2}}{\sqrt{6}-\sqrt{3}}=\frac{\sqrt{2}(\sqrt{2}-1)}{\sqrt{3}(\sqrt{2}-1)}=\frac{\sqrt{2}}{\sqrt{3}}= \sqrt{ \frac{2}{3} }=ili =\frac{\sqrt{3}*\sqrt{2}}{\sqrt{3}*\sqrt{3}}=\frac{\sqrt{6}}{3}$

в)
$\frac{x^2-2}{\sqrt{2}x+2}=\frac{(x-\sqrt{2})(x+\sqrt{2})}{\sqrt{2}(x+\sqrt{2})}=\frac{x-\sqrt{2}}{\sqrt{2}}$

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