[tex] \frac{ {2x}^{2} - x - 15 }{ {2x}^{2} - 7x + 3 } = \frac{ {2x}^{2} - 6x + 5x - 15 }{ {2x}^{2} - 6x - x + 3 } = \frac{2x( \frac{ {2x}^{2} }{2x} - \frac{2 \times 3x}{2x}) + 5( \frac{5x}{5} - \frac{3 \times 5}{5}) }{2x( \frac{ {2x}^{2} }{2x} - \frac{2 \times 3x}{2x}) + ( - x + 3) } = \frac{2x( {x}^{2 - 1} - 3) + 5(x - 3) }{2x( {x}^{2 - 1} - 3) + ( - x + 3) } = \frac{2x(x - 3) + 5(x - 3)}{2x(x - 3) + ( - x + 3)} = \frac{(x - 3)( \frac{2x(x - 3)}{x - 3} + \frac{5(x - 3)}{x - 3}) }{(x - 3)( \frac{2x(x - 3)}{x - 3} + \frac{ - x + 3}{x - 3}) } = \frac{(x - 3)(2x + 5)}{(x - 3)(2x - 1)} = \frac{2x + 5}{2x - 1} [/tex]
