Question

(г) к делить на х+√к (д) 5 делить на √13+√3 (е) 6 делить на 5-2√6

Answer 1

Ответ:

$\frac{k(x-\sqrt{k})}{x^{2}-k};$

$\frac{\sqrt{13}-\sqrt{3}}{2};$

$30+12\sqrt{6};$

Объяснение:

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

$\frac{5}{\sqrt{13}+\sqrt{3}}=\frac{5(\sqrt{13}-\sqrt{3})}{(\sqrt{13}+\sqrt{3})(\sqrt{13}-\sqrt{3})}=\frac{5(\sqrt{13}-\sqrt{3})}{(\sqrt{13})^{2}-(\sqrt{3})^{2}}=\frac{5(\sqrt{13}-\sqrt{3})}{13-3}=\frac{5(\sqrt{13}-\sqrt{3})}{10}=$

$=\frac{\sqrt{13}-\sqrt{3}}{2};$

$\frac{6}{5-2\sqrt{6}}=\frac{6(5+2\sqrt{6})}{(5-2\sqrt{6})(5+2\sqrt{6})}=\frac{6(5+2\sqrt{6})}{5^{2}-(2\sqrt{6})^{2}}=\frac{6(5+2\sqrt{6})}{25-24}=30+12\sqrt{6};$