Скоротіть дріб:
1) $\frac{y-36}{y-6\sqrt y};$
2) $\frac{a-6\sqrt a\sqrt b+9b}{a-9b};$
3) $\frac{\sqrt{26}+13}{2+\sqrt{26}}.$
Розв'язок:
1) $\frac{y-36}{y-6\sqrt y}=\frac{(\sqrt y-6)(\sqrt y+6)}{\sqrt y(\sqrt y-6)}=\frac{\sqrt y+6}{\sqrt y};$
2) $\frac{a-6\sqrt a\sqrt b+9b}{a-9b}=$
$= \frac{(\sqrt a-3\sqrt b)^2}{(\sqrt a-3\sqrt b)(\sqrt a+3\sqrt b)}=$
$= \frac{\sqrt a-3\sqrt b}{\sqrt a+3\sqrt b};$
3) $\frac{\sqrt{26}+13}{2+\sqrt{26}}=\frac{\sqrt{13}\sqrt2+\sqrt{13}\sqrt{13}}{\sqrt2\sqrt2+\sqrt{13}\sqrt2}=$
$= \frac{\sqrt{13}(\sqrt2+\sqrt{13})}{\sqrt2(\sqrt2+\sqrt{13})}=\frac{\sqrt{13}}{\sqrt2}=$
$= \sqrt{\frac{13}{2}}=\sqrt{6{,}5}.$