Question

даю 100 баллов

нужно решить 2,3 и 4
​

Answer 1

2)

$\frac{5}{a} + \frac{a - 5}{a + 2} = \frac{5(a + 2) + a(a - 5)}{a(a + 2)} = \frac{5a + 10 + {a}^{2} - 5a }{ {a}^{2} + 2a } = \\ = \frac{ {a}^{2} + 10 }{ {a}^{2} + 2a}$

$\frac{ 2{x}^{2} }{ {x}^{2} - 4 } - \frac{2x}{x + 2} = \frac{2 {x}^{2} }{(x - 2)(x + 2)} - \frac{2x}{x + 2} = \frac{2 {x}^{2} - 2x(x - 2)}{(x - 2)(x + 2)} = \\ = \frac{2 {x}^{2} - 2 {x}^{2} + 4x }{ {x}^{2} - 4} = \frac{4x}{ {x}^{2} - 4}$

3)

$\frac{ {y}^{2} + 10y + 25 }{ {y}^{2} - 25 } \div \frac{10y - 50}{ {y}^{2} + 5y } = \frac{(y - 5) {}^{2} }{(y - 5)(y + 5)} \times \frac{y(y + 5)}{10(y - 5)} = \\ = \frac{y}{10} = \frac{40}{10} = 4$

4)

$\frac{x}{y} = c \\ y = \frac{x}{c} \\ \frac{y}{z} = \frac{1}{c} \\ \frac{ \frac{x}{c} }{z} = \frac{1}{c} \\ \frac{x}{cz} = \frac{1}{c} \: \: | \times c \\ \frac{x}{z} = 1$