Ответ:

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

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

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

[tex] \frac{4a \times (a + 1) - 3a - 3}{(a - 1) \times (a + 1)} [/tex]

[tex] \frac{4a \times (a + 1) - 3( a + 1)}{(a - 1) \times (a + 1)} [/tex]

[tex] \frac{(a + 1) \times (4a - 3)}{(a - 1) \times (a + 1)} [/tex]

Сокращаем на общий делитель a+1:

[tex] \frac{4a - 3}{a - 1} [/tex]