Разложим на множители числитель:

[tex] - {x}^{2} + 5x - 6 = 0 \\ x {}^{2} - 5x + 6 = 0 \\ d =( - 5) { }^{2} - 4 \times 1 \times 6 = 25 - 2 = 1 \\ x _{1} = \frac{5 + 1}{2} = \frac{6}{2} = 3 \\ x_{2} = \frac{5 - 1}{2} = \frac{4}{2} = 2 \\ - {x}^{2} + x - 6 = - (x - 2)(x - 3)[/tex]

Теперь запишем дробь:

[tex] \frac{5x - {x}^{2} - 6 }{ {x}^{2} - 4 } = \frac{ - (x - 2)(x - 3)}{(x - 2)(x + 2)} = \\ \frac{ - (x - 3)}{x + 2} = \frac{3 - x}{x + 2} [/tex]