Question

7/√7 - 2/(√7 - √5) + 4/(√5 + √3) самый первый пример на картинке

Answer 1

$\frac{7}{ \sqrt{7} }- \frac{2}{ \sqrt{7}- \sqrt{5}}+ \frac{4}{ \sqrt{5}+ \sqrt{3}}= \\ \\ = \frac{7 \sqrt{7} }{ \sqrt{7}\cdot \sqrt{7} }- \frac{2(\sqrt{7}+\sqrt{5})}{ (\sqrt{7}- \sqrt{5})(\sqrt{7}+ \sqrt{5})}+ \frac{4(\sqrt{5}- \sqrt{3})}{ (\sqrt{5}+ \sqrt{3})(\sqrt{5}- \sqrt{3})}= \\ \\ =$
$=\sqrt{7} - \frac{2(\sqrt{7}+\sqrt{5})}{ (\sqrt{7})^2- (\sqrt{5})^2}+ \frac{4(\sqrt{5}- \sqrt{3})}{ (\sqrt{5})^2-( \sqrt{3})^2}= \sqrt{7}-\frac{2(\sqrt{7}+\sqrt{5})}{ 2}+ \frac{4(\sqrt{5}- \sqrt{3})}{ 2}=$
$= \sqrt{7}- \sqrt{7}- \sqrt{5}+2 \sqrt{5}-2 \sqrt{3}= \sqrt{5}-2 \sqrt{3}$