8. Выполните действия: a) $$\frac{5}{3x} + \frac{2}{7x^2}$$; б) $$\frac{1}{x-3} - \frac{1}{x+3}$$; в) $$7a^3 \cdot \frac{3b}{14a^2}$$; г) $$\frac{12xy^2}{5a^3} : \frac{24y}{25a^2b}$$

Решение:

1. \(\frac{5}{3x} + \frac{2}{7x^2} = \frac{5 \cdot 7x}{3x \cdot 7x} + \frac{2 \cdot 3}{7x^2 \cdot 3} = \frac{35x + 6}{21x^2}\)
2. \(\frac{1}{x-3} - \frac{1}{x+3} = \frac{(x+3) - (x-3)}{(x-3)(x+3)} = \frac{x+3-x+3}{x^2-9} = \frac{6}{x^2-9}\)
3. \(7a^3 \cdot \frac{3b}{14a^2} = \frac{7a^3 \cdot 3b}{14a^2} = \frac{21a^3b}{14a^2} = \frac{3ab}{2}\)
4. \(\frac{12xy^2}{5a^3} : \frac{24y}{25a^2b} = \frac{12xy^2}{5a^3} \cdot \frac{25a^2b}{24y} = \frac{12xy^2 \cdot 25a^2b}{5a^3 \cdot 24y} = \frac{300xy^2a^2b}{120a^3y} = \frac{5xyb}{2a}\)

Ответ: а) \(\frac{35x + 6}{21x^2}\); б) \(\frac{6}{x^2-9}\); в) \(\frac{3ab}{2}\); г) \(\frac{5xyb}{2a}\).