5. Сократить дроби √x + √y;c+2√cd+d;b-25 x-y;c-d;√6+5

5. Сократим дроби:

1. $$\frac{√x + √y}{x - y} = \frac{√x + √y}{(√x)^2 - (√y)^2} = \frac{√x + √y}{(√x - √y)(√x + √y)} = \frac{1}{√x - √y}$$
2. $$\frac{c + 2√{cd} + d}{c - d} = \frac{(√c)^2 + 2√c \cdot √d + (√d)^2}{(√c)^2 - (√d)^2} = \frac{(√c + √d)^2}{(√c - √d)(√c + √d)} = \frac{√c + √d}{√c - √d}$$
3. $$\frac{b - 25}{√b + 5} = \frac{(√b)^2 - 5^2}{√b + 5} = \frac{(√b - 5)(√b + 5)}{√b + 5} = √b - 5$$

Ответ: $$\frac{1}{√x - √y}; \frac{√c + √d}{√c - √d}; √b - 5$$