[tex] \frac{ {x}^{2} - 9 }{ {x}^{2} - 5x + 6 } = \frac{ {x}^{2} - {3}^{2} }{ {x}^{2} - 3x - 2x + 6 } = \frac{(x - 3)(x + 3)}{x( \frac{ {x}^{2} }{x} - \frac{3x}{x}) + 2( - \frac{2x}{2} + \frac{2 \times 3}{2}) } = \frac{(x - 3)(x + 3)}{x( {x}^{2 - 1} - 3) + 2( - x + 3) } = \frac{(x - 3)(x + 3)}{x(x - 3) + 2( - x + 3)} = \frac{(x - 3)(x + 3)}{(x - 3)( \frac{x(x - 3)}{x - 3} + \frac{2( - x + 3)}{x - 3}) } = \frac{(x - 3)(x + 3)}{(x - 3)(x - 2)} = \frac{x + 3}{x - 2} [/tex]
