4. Сократить дроби: (√30 + √35)/(√12 + √14); (√x + √y)/(x − y); (c + 2√cd + d)/(c − d); (b − 25)/(√b + 5).

1. \(\frac{\sqrt{30}+\sqrt{35}}{\sqrt{12}+\sqrt{14}}=\frac{\sqrt5(\sqrt6+\sqrt7)}{\sqrt2(\sqrt6+\sqrt7)}=\frac{\sqrt5}{\sqrt2}=\frac{\sqrt{10}}2\).
2. При \(x,y\geq0\) и \(x\ne y\): \(\frac{\sqrt{x}+\sqrt{y}}{x-y}=\frac{\sqrt{x}+\sqrt{y}}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}=\frac1{\sqrt{x}-\sqrt{y}}\).
3. При \(c,d\geq0\) и \(c\ne d\): \(\frac{c+2\sqrt{cd}+d}{c-d}=\frac{(\sqrt c+\sqrt d)^2}{(\sqrt c-\sqrt d)(\sqrt c+\sqrt d)}=\frac{\sqrt c+\sqrt d}{\sqrt c-\sqrt d}\).
4. При \(b\geq0\): \(\frac{b-25}{\sqrt b+5}=\frac{(\sqrt b-5)(\sqrt b+5)}{\sqrt b+5}=\sqrt b-5\).

Ответ: \(\frac{\sqrt{10}}2;\ \frac1{\sqrt{x}-\sqrt{y}};\ \frac{\sqrt c+\sqrt d}{\sqrt c-\sqrt d};\ \sqrt b-5\).