Question

Буду благодарна за помощь.
Докажи тождество:

Answer 1

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