Question

Помогите с 912 пожалуйста

Answer 1

а)
$\frac{ {x}^{2} - 4x}{ {x}^{2} + 7x } \div \frac{24 - 6x}{49 - {x}^{2} } = \frac{x(x - 4)}{x(x + 7)} \div \frac{4(4 - x)}{(7 - x)(7 + x)} = - \frac{x(x - 4)}{x + 7} \times \frac{(7 - x)(7 + x)}{4(x - 4)} = - \frac{x(7 - x)}{4}$
б)
$\frac{ {y}^{3} - 16y}{2y + 18} \div \frac{4 - y}{ {y}^{2} + 9y } = \frac{ {y}^{3} - 16y}{2y + 18} \times \frac{ {y}^{2} + 9y}{4 - y} = \frac{y( {y}^{2} - 16)}{2(y + 9)} \times \frac{y(y + 9)}{4 - y} = - \frac{y(y - 4)(y + 4)}{2} \times \frac{y}{y - 4} = - \frac{ {y}^{2} (y + 4)}{2}$
в)
$\frac{(a + b)^{2} - 2ab}{4 {a}^{2} } \div \frac{ {a}^{2} + {b}^{2} }{ab} = \frac{ {a}^{2} + 2ab + {b}^{2} - 2ab }{ 4{a}^{2} } \times \frac{ab}{ {a}^{2} + {b}^{2} } = \frac{ {a}^{2} + {b}^{2} }{4a} \times \frac{b}{ {a}^{2} + {b}^{2} } = \frac{b}{4a}$
г)
$\frac{5 {c}^{3} - 5 }{c + 2} \div \frac{ {(c + 1)}^{2} - c}{13c + 26} = \frac{5( {c}^{3} - 1)}{c + 2} \times \frac{13(c + 2)}{ {c}^{2} + 2c + 1 - c} = \frac{5(c - 1)( {c}^{2} + c + 1)}{c + 2} \times \frac{13(c + 2)}{ {c}^{2} + c + 1} = 65(c - 1)$