Question

Упростите выражение : ​

Answer 1

1)

$\frac{ab + {b}^{2} }{3} \div \frac{ {b}^{3} }{3a} + \frac{a + b}{b} = \frac{b(a + b)}{3} \times \frac{3a}{ {b}^{3} } + \frac{a + b}{b} = \frac{a(a + b)}{ {b}^{2} } + \frac{a + b}{b} = \frac{a(a + b) + b(a + b)}{ {b}^{2} } = \frac{(a + b)(a + b)}{ {b}^{2} } = \frac{ {a}^{2} + 2ab + {b}^{2} }{ {b}^{2} }$

2)

$( \frac{a}{a + 4} - \frac{a}{a - 4} ) \times \frac{a + 4}{a} = \frac{a(a - 4) - a(a + 4)}{(a + 4)(a - 4)} \times \frac{a + 4}{a} = \frac{ {a}^{2} - 4a - {a}^{2} - 4a}{(a + 4)(a - 4)} \times \frac{a + 4}{a} = \frac{ - 8a}{(a + 4)(a - 4)} \times \frac{a + 4}{a} = \frac{ - 8}{a - 4}$