37. Выполните деление:

Решение:

• а) \[ \frac{m^2 - 3m}{8x^2} : \frac{3m}{8x} = \frac{m(m - 3)}{8x^2} \cdot \frac{8x}{3m} = \frac{m - 3}{3x} \]
• б) \[ \frac{5a^2}{6b^3} : \frac{a^3}{ab - b^2} = \frac{5a^2}{6b^3} \cdot \frac{b(a - b)}{a^3} = \frac{5b(a - b)}{6b^3 a} = \frac{5(a - b)}{6b^2 a} \]
• в) \[ \frac{x^2 + x^3}{11a^2} : \frac{4 + 4x}{a^3} = \frac{x^2(1 + x)}{11a^2} \cdot \frac{a^3}{4(1 + x)} = \frac{x^2 a}{44} \]
• г) \[ \frac{6ax}{m^2 - 2m} : \frac{8ax}{3m - 6} = \frac{6ax}{m(m - 2)} \cdot \frac{3(m - 2)}{8ax} = \frac{6ax · 3(m - 2)}{m(m - 2) · 8ax} = \frac{18}{8m} = \frac{9}{4m} \]
• д) \[ \frac{a^2 - 3ab}{3b} : (7a - 21b) = \frac{a(a - 3b)}{3b} \cdot \frac{1}{7(a - 3b)} = \frac{a}{21b} \]
• е) \[ (x^2 - 4y^2) : \frac{5x - 10y}{x} = (x - 2y)(x + 2y) \cdot \frac{x}{5(x - 2y)} = \frac{x(x + 2y)}{5} \]
• ж) \[ (2a - b)^2 : \frac{4a^3 - ab^2}{3} = (2a - b)^2 \cdot \frac{3}{a(4a^2 - b^2)} = (2a - b)^2 \cdot \frac{3}{a(2a - b)(2a + b)} = \frac{3(2a - b)}{a(2a + b)} \]
• з) \[ (10m - 15n) : \frac{(2m - 3n)^2}{2m} = 5(2m - 3n) \cdot \frac{2m}{(2m - 3n)^2} = \frac{10m}{2m - 3n} \]