Скоротіть дріб:
1) $\frac{a+5\sqrt a}{a-25};$
2) $\frac{x-4y}{x+4\sqrt x\sqrt y+4y};$
3) $\frac{\sqrt{21}-3}{7-\sqrt{21}}.$
Розв'язок:
1) $\frac{a+5\sqrt a}{a-25}=\frac{\sqrt a(\sqrt a+5)}{(\sqrt a-5)(\sqrt a+5)}=\frac{\sqrt a}{\sqrt a-5};$
2) $\frac{x-4y}{x+4\sqrt x\sqrt y+4y}=$
$= \frac{(\sqrt x-2\sqrt y)(\sqrt x+2\sqrt y)}{(\sqrt x+2\sqrt y)^2}=$
$= \frac{\sqrt x-2\sqrt y}{\sqrt x+2\sqrt y};$
3) $\frac{\sqrt{21}-3}{7-\sqrt{21}}=\frac{\sqrt3\sqrt7-\sqrt3\sqrt3}{\sqrt7\sqrt7-\sqrt3\sqrt7}=$
$= \frac{\sqrt3(\sqrt7-\sqrt3)}{\sqrt7(\sqrt7-\sqrt3)}=\frac{\sqrt3}{\sqrt7}=\sqrt{\frac{3}{7}}.$