29. Упростите выражение: 3) \(\frac{x^2 - 49}{x^2 + 9x} \cdot \frac{x^2 - 81}{x^2 - 7x}\) 4) \(\frac{3b^2 + 6b + 3}{b^3 - 8} \cdot \frac{2b^2 + 4b + 8}{9b + 9}\)

Решение:

1. \( \frac{x^2 - 49}{x^2 + 9x} \cdot \frac{x^2 - 81}{x^2 - 7x} = \frac{(x - 7)(x + 7)}{x(x + 9)} \cdot \frac{(x - 9)(x + 9)}{x(x - 7)} = \frac{(x + 7)(x - 9)}{x^2} \)
2. \( \frac{3b^2 + 6b + 3}{b^3 - 8} \cdot \frac{2b^2 + 4b + 8}{9b + 9} = \frac{3(b^2 + 2b + 1)}{(b - 2)(b^2 + 2b + 4)} \cdot \frac{2(b^2 + 2b + 4)}{9(b + 1)} = \frac{3(b + 1)^2}{(b - 2)(b^2 + 2b + 4)} \cdot \frac{2(b^2 + 2b + 4)}{9(b + 1)} = \frac{3(b + 1)^2 \cdot 2 \cdot (b^2 + 2b + 4)}{(b - 2)(b^2 + 2b + 4) \cdot 9(b + 1)} = \frac{6(b + 1)}{9(b - 2)} = \frac{2(b + 1)}{3(b - 2)} \)

Ответ: 3) \(\frac{(x + 7)(x - 9)}{x^2}\); 4) \(\frac{2(b + 1)}{3(b - 2)}\).