Question

Срочно вщытащту ( алгебра )
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Answer 1

1)

Умножаем и числитель и знаменатель

на$\sqrt{3}-1$

$\frac{4}{\sqrt{3}+1}= \frac{4(\sqrt{3}-1) }{(\sqrt{3}+1 )(\sqrt{3}-1)}= \frac{4(\sqrt{3}-1) }{(\sqrt{3})^2-1^2}=\frac{4(\sqrt{3}-1) }{3-1}=2(\sqrt{3}-1)$

2)

$\frac{1}{1-\sqrt{2} } =\frac{1+\sqrt{2} }{(1-\sqrt{2})(1+\sqrt{2}) }= \frac{1+\sqrt{2} }{1^2-(\sqrt{2})^2) }= \frac{1+\sqrt{2} }{1-2 }= -(1+\sqrt{2})=-1-\sqrt{2}$

3)

$\frac{1}{\sqrt{x} -\sqrt{y} } =\frac{\sqrt{x} +\sqrt{y} }{x-y}$

4)

$\frac{a}{\sqrt{a}+\sqrt{b} }= \frac{a(\sqrt{a}-\sqrt{b} )}{(\sqrt{a}+\sqrt{b} )(\sqrt{a}-\sqrt{b}) }= \frac{a(\sqrt{a}-\sqrt{b} )}{a-b}$