Question

Буду благодарна за помощь.
Докажи тождество:

Answer 1

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