9. $$\frac{b}{24b-64} : \frac{9b^2}{9b^2-64}$$ 10. $$\frac{b}{4b-1} : \frac{16b^2}{16b^2-1}$$ Выполните умножение: 1. $$\frac{100a^2-b^2}{6a^2} \cdot \frac{a}{20a-2b}$$ 2. $$\frac{49a^2-b^2}{4a^2} \cdot \frac{a}{63a-9b}$$ 3. $$\frac{9a^2-b^2}{7a^2} \cdot \frac{a}{24a-8b}$$ 4. $$\frac{4a^2-b^2}{6a^2} \cdot \frac{a}{6a-3b}$$ 5. $$\frac{49a^2-b^2}{8a^2} \cdot \frac{a}{14a-2b}$$ 6. $$\frac{a^2-4b^2}{4a} \cdot (ab-2b^2)$$ 7. $$\frac{a^2-25b^2}{7a} \cdot (ab+5b^2)$$ 8. $$\frac{a^2-100b^2}{3a} \cdot (ab-10b^2)$$ 9. $$\frac{b}{a-b} \cdot (\frac{1}{a} - \frac{1}{b})$$ 10. $$\frac{b}{2a-b} \cdot (\frac{1}{a} - \frac{2}{b})$$ Найдите разность: 1. $$\frac{1}{7x} - \frac{5x+y}{7xy}$$ 2. $$\frac{1}{6x} - \frac{6x+y}{6xy}$$ 3. $$\frac{1}{3x} - \frac{-x+y}{3xy}$$ 4. $$\frac{1}{8x} - \frac{7x+y}{8xy}$$ 5. $$\frac{1}{7x} - \frac{2x+y}{7xy}$$ 6. $$\frac{28x^2}{7x-7} - 4x$$ 7. $$\frac{30x^2}{5x+11} - 6x$$

Предмет: Математика

9. $$\frac{b}{24b-64} : \frac{9b^2}{9b^2-64} = \frac{b}{8(3b-8)} \cdot \frac{(3b-8)(3b+8)}{9b^2} = \frac{3b+8}{72b}$$

10. $$\frac{b}{4b-1} : \frac{16b^2}{16b^2-1} = \frac{b}{4b-1} \cdot \frac{(4b-1)(4b+1)}{16b^2} = \frac{4b+1}{16b}$$

Выполните умножение:

1. $$\frac{100a^2-b^2}{6a^2} \cdot \frac{a}{20a-2b} = \frac{(10a-b)(10a+b)}{6a^2} \cdot \frac{a}{2(10a-b)} = \frac{10a+b}{12a}$$

2. $$\frac{49a^2-b^2}{4a^2} \cdot \frac{a}{63a-9b} = \frac{(7a-b)(7a+b)}{4a^2} \cdot \frac{a}{9(7a-b)} = \frac{7a+b}{36a}$$

3. $$\frac{9a^2-b^2}{7a^2} \cdot \frac{a}{24a-8b} = \frac{(3a-b)(3a+b)}{7a^2} \cdot \frac{a}{8(3a-b)} = \frac{3a+b}{56a}$$

4. $$\frac{4a^2-b^2}{6a^2} \cdot \frac{a}{6a-3b} = \frac{(2a-b)(2a+b)}{6a^2} \cdot \frac{a}{3(2a-b)} = \frac{2a+b}{18a}$$

5. $$\frac{49a^2-b^2}{8a^2} \cdot \frac{a}{14a-2b} = \frac{(7a-b)(7a+b)}{8a^2} \cdot \frac{a}{2(7a-b)} = \frac{7a+b}{16a}$$

6. $$\frac{a^2-4b^2}{4a} \cdot (ab-2b^2) = \frac{(a-2b)(a+2b)}{4a} \cdot b(a-2b) = \frac{b(a-2b)^2(a+2b)}{4a}$$

7. $$\frac{a^2-25b^2}{7a} \cdot (ab+5b^2) = \frac{(a-5b)(a+5b)}{7a} \cdot b(a+5b) = \frac{b(a-5b)(a+5b)^2}{7a}$$

8. $$\frac{a^2-100b^2}{3a} \cdot (ab-10b^2) = \frac{(a-10b)(a+10b)}{3a} \cdot b(a-10b) = \frac{b(a-10b)^2(a+10b)}{3a}$$

9. $$\frac{b}{a-b} \cdot (\frac{1}{a} - \frac{1}{b}) = \frac{b}{a-b} \cdot (\frac{b-a}{ab}) = \frac{b}{a-b} \cdot (\frac{-(a-b)}{ab}) = -\frac{b}{ab} = -\frac{1}{a}$$

10. $$\frac{b}{2a-b} \cdot (\frac{1}{a} - \frac{2}{b}) = \frac{b}{2a-b} \cdot (\frac{b-2a}{ab}) = \frac{b}{2a-b} \cdot (\frac{-(2a-b)}{ab}) = -\frac{b}{ab} = -\frac{1}{a}$$

Найдите разность:

1. $$\frac{1}{7x} - \frac{5x+y}{7xy} = \frac{y - (5x+y)}{7xy} = \frac{y-5x-y}{7xy} = \frac{-5x}{7xy} = -\frac{5}{7y}$$

2. $$\frac{1}{6x} - \frac{6x+y}{6xy} = \frac{y - (6x+y)}{6xy} = \frac{y-6x-y}{6xy} = \frac{-6x}{6xy} = -\frac{1}{y}$$

3. $$\frac{1}{3x} - \frac{-x+y}{3xy} = \frac{y - (-x+y)}{3xy} = \frac{y+x-y}{3xy} = \frac{x}{3xy} = \frac{1}{3y}$$

4. $$\frac{1}{8x} - \frac{7x+y}{8xy} = \frac{y - (7x+y)}{8xy} = \frac{y-7x-y}{8xy} = \frac{-7x}{8xy} = -\frac{7}{8y}$$

5. $$\frac{1}{7x} - \frac{2x+y}{7xy} = \frac{y - (2x+y)}{7xy} = \frac{y-2x-y}{7xy} = \frac{-2x}{7xy} = -\frac{2}{7y}$$

6. $$\frac{28x^2}{7x-7} - 4x = \frac{28x^2 - 4x(7x-7)}{7x-7} = \frac{28x^2 - 28x^2 + 28x}{7x-7} = \frac{28x}{7(x-1)} = \frac{4x}{x-1}$$

7. $$\frac{30x^2}{5x+11} - 6x = \frac{30x^2 - 6x(5x+11)}{5x+11} = \frac{30x^2 - 30x^2 - 66x}{5x+11} = \frac{-66x}{5x+11}$$