Question

Спростити вираз:
$\frac{a + \sqrt{ab} }{b + \sqrt{ab} }$
де а>0,b>0;​

Answer 1

......................

Answer 2

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