3. Сократите дробь: а) \(\frac{\sqrt3-3}{\sqrt5-\sqrt{15}}\); б) \(\frac{a-2\sqrt a}{3\sqrt a-6}\).

а) \(\frac{\sqrt3-3}{\sqrt5-\sqrt{15}}=\frac{\sqrt3-3}{\sqrt5(1-\sqrt3)}=\frac{-(3-\sqrt3)}{-\sqrt5(\sqrt3-1)}=\frac{\sqrt3(\sqrt3-1)}{\sqrt5(\sqrt3-1)}=\frac{\sqrt3}{\sqrt5}=\frac{\sqrt{15}}5\).

б) При \(a\geq0\) и \(a\ne4\): \(\frac{a-2\sqrt a}{3\sqrt a-6}=\frac{\sqrt a(\sqrt a-2)}{3(\sqrt a-2)}=\frac{\sqrt a}{3}\).

Ответ: а) \(\frac{\sqrt{15}}5\); б) \(\frac{\sqrt a}{3}\), \(a\geq0,\ a\ne4\).