5. Сократить дроби √30+√35 √12+√14 ; b-25 √চ+5 ; √x + √y x-y ; c+ 2√cd + d c-d ;

5. Сократим дроби.

• $$\frac{√30+√35}{√12+√14} = \frac{√(5\cdot6)+√(5\cdot7)}{√(2\cdot6)+√(2\cdot7)} = \frac{√5(√6+√7)}{√2(√6+√7)} = \frac{√5}{√2} = \frac{√5\cdot√2}{√2\cdot√2} = \frac{√10}{2}$$
• $$\frac{b-25}{√b+5} = \frac{(√b)^2 - 5^2}{√b+5} = \frac{(√b-5)(√b+5)}{√b+5} = √b-5$$
• $$\frac{√x + √y}{x-y} = \frac{√x + √y}{(√x)^2 - (√y)^2} = \frac{√x + √y}{(√x - √y)(√x + √y)} = \frac{1}{√x - √y}$$
• $$\frac{c+ 2√{cd} + d}{c-d} = \frac{(√c)^2 + 2√c√d + (√d)^2}{(√c)^2 - (√d)^2} = \frac{(√c + √d)^2}{(√c - √d)(√c + √d)} = \frac{√c + √d}{√c - √d}$$

Ответ: $$\frac{√10}{2}; √b-5; \frac{1}{√x - √y}; \frac{√c + √d}{√c - √d}$$