Step-by-step explanation:
[tex] \frac{x + 1}{x - 4} - \frac{x + 3}{x + 2} \\ \frac{(x + 1)(x + 2)}{(x - 4)(x + 2)} - \frac{(x + 3)(x - 4)}{(x + 2)(x - 4)} \\ \frac{ {x}^{2} + 3x + 2 }{(x + 2)(x - 4)} - \frac{ {x}^{2} - x - 12 }{(x + 2)(x - 4)} \\ \frac{( {x}^{2} + 3x + 2) - ( {x}^{2} - x - 12)}{(x + 2)(x - 4)} \\ \frac{ {x}^{2} + 3x + 2 - {x}^{2} + x + 12}{(x + 2)(x - 4)} \\ \frac{4x + 14}{(x + 2)(x - 4)} \\ \frac{2(2x + 7)}{(x + 2)(x - 4)} [/tex]
