Question

Помогите сократить!Срочно!!
9 класс

Answer 1

$( \frac{a - 1}{a + 1} - \frac{a {}^{3} + 1 }{ {a}^{2} - 1 } \times \frac{a - 1}{a {}^{2} + a + 1 }) \div \frac{a}{1 + a} = - \frac{2}{a {}^{3} + {a}^{2} + a } \: \\ 1)\frac{a {}^{3} + 1 }{ {a}^{2} - 1 } \times \frac{a - 1}{a {}^{2} + a + 1 } =\frac{(a + 1)( a {}^{2} - a + 1) }{ (a - 1)(a + 1)} \times \frac{a - 1}{a {}^{2} + a + 1 } = \frac{a {}^{2} - a + 1 }{a {}^{2} + a + 1 } \\ 2) \frac{a - 1}{a + 1} - \frac{a {}^{2} - a + 1 }{a {}^{2} + a + 1 } = \frac{(a {}^{3} - 1) - (a {}^{3} + 1)}{(a + 1)(a {}^{2} + a + 1) } = \frac{ a {}^{3} - 1 - a {}^{3} - 1}{(a + 1)(a {}^{2} + a + 1) } = \frac{ - 2}{(a + 1)(a {}^{2} + a + 1) } \\ 3)\frac{ - 2}{(a + 1)(a {}^{2} + a + 1) } \div \frac{a}{1 + a} = \frac{ - 2}{(a + 1)(a {}^{2} + a + 1) } \times \frac{a + 1}{a} = \frac{ - 2}{(a {}^{2} + a + 1) \times a} = - \frac{2}{a {}^{3} + {a}^{2} + a }$