Ответ:

[tex] \frac{4 {a}^{2} + a - 3 }{ {a}^{2} - 1} = \frac{4 {a}^{2} + 4a - 3a - 3 }{ {a}^{2} - 1} = \frac{4a(a + 1) - 3(a + 1)}{(a - 1)(a + 1)} = \frac{(4a - 3)(a + 1)}{(a - 1)(a + 1)} = \frac{4a - 3}{a - 1} .[/tex]