Решите пример пожалуйста

Ответ:

$\frac{12}{5x} \times \frac{ {x}^{3} }{12a} = \frac{ {x}^{2} }{5a} \\ \frac{14 {a}^{2} b }{ 3{x}^{3} } \times \frac{8 {x}^{2} }{21 {a}^{2}b } = \frac{2 \times 8}{3x \times 3} = \frac{16}{9x} \\ \frac{ {x}^{2} - xy }{y} \times \frac{ {y}^{2} }{x} = \frac{x(x - y)}{y} \times \frac{ {y}^{2} }{x} = (x - y) \times y = xy - {y}^{2}$

$\frac{ {a}^{2} - 1}{a - b} \times \frac{7a - 7b}{ {a}^{2} + a } = \frac{(a + 1)(a - 1)}{a - b} \times \frac{7(a - b)}{a(a + 1)} = \frac{a - 1}{a}$

$\frac{ax + ay}{ {x}^{2} - 2xy + {y}^{2} } \times \frac{ {x}^{2} - xy }{7x + 7y} = \frac{a(x + y)}{ {(x - y)}^{2} } \times \frac{x(x - y)}{7(x + y)} = \frac{ax}{(x - y) \times 7} = \frac{ax}{7x - 7y}$

$\frac{14}{9 {x}^{3} } \div \frac{7x}{2 {y}^{2} } = \frac{14}{9 {x}^{3} } \times \frac{2 {y}^{2} }{7x} = \frac{4 {y}^{2} }{9 {x}^{4} }$

$\frac{ {x}^{2} - 4 {y}^{2} }{xy} \div \frac{ {x}^{2} - 2xy }{3y} = \frac{ (x - 2y)(x + 2y)}{xy} \times \frac{3y}{x(x - 2y)} = \frac{(x + 2y) \times 3y}{xy \times x} = \frac{3xy + 6 {y}^{2} }{ {x}^{2} y}$

$\frac{3x + 6y}{ {x}^{2} - {y}^{2} } \div \frac{5x + 10y}{ {x}^{2} - 2xy + {y}^{2} } = \frac{3(x + 2y)}{(x - y)(x + y)} \times \frac{ {(x - y)}^{2} }{5( x + 2y) } = \frac{3(x - y)}{(x + y) \times 5} = \frac{3x - 3y}{5x + 5y}$