11. Сократить дроби: а) (√35 − √15)/(√14 − √6); б) (x − 2√xy + y)/(x − y); в) (a − 9)/(√a + 3); г) (√a − √b)/(a − b).

1. \(\frac{\sqrt{35}-\sqrt{15}}{\sqrt{14}-\sqrt6}=\frac{\sqrt5(\sqrt7-\sqrt3)}{\sqrt2(\sqrt7-\sqrt3)}=\sqrt{\frac52}=\frac{\sqrt{10}}2\).
2. При \(x,y\ge0\) и \(x\ne y\): \(\frac{x-2\sqrt{xy}+y}{x-y}=\frac{(\sqrt{x}-\sqrt{y})^2}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}=\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\).
3. При \(a\ge0\): \(\frac{a-9}{\sqrt a+3}=\frac{(\sqrt a-3)(\sqrt a+3)}{\sqrt a+3}=\sqrt a-3\).
4. При \(a,b\ge0\) и \(a\ne b\): \(\frac{\sqrt a-\sqrt b}{a-b}=\frac{\sqrt a-\sqrt b}{(\sqrt a-\sqrt b)(\sqrt a+\sqrt b)}=\frac1{\sqrt a+\sqrt b}\).

Ответ: а) \(\frac{\sqrt{10}}2\); б) \(\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\); в) \(\sqrt a-3\); г) \(\frac1{\sqrt a+\sqrt b}\).