[tex] \frac{5}{x - 3} - \frac{x - 2}{ {x}^{2} - 9 } + \frac{x - 1}{2x + 6} = \frac{5}{x - 3} - \frac{x - 2}{(x - 3)(x + 3)} + \frac{x - 1}{2(x + 3)} = \frac{10(x + 3) - 2(x - 2) + (x - 1)(x - 3)}{2(x - 3)(x + 3)} = \frac{10x + 30 - 2x + 4 + {x}^{2} - 3x - x + 3}{2( {x}^{2} - 9) } = \frac{ {x}^{2} + 4x + 37}{2 {x}^{2} - 18 } [/tex]