[tex]a) \: \frac{2}{x - 5} = \frac{3}{4 + x} \\ 2(4 + x) = 3(x - 5) \\ 8 + 2x = 3x - 15 \\ 2x - 3x = - 15 - 8 \\ - x = - 23 \\ x = 23 \\ \\ b) \: \frac{3}{2x - 5} = \frac{ - 1}{x + 7} \\ 3(x + 7) = - 1(2x - 5) \\ 3x + 21 = - 2x + 5 \\ 3x + 2x = 5 - 21 \\ 5x = - 16 \\ x = - \frac{16}{5} \\ \\ c) \: ( {x}^{2} - 9) \times \frac{5}{x + 3} + ( {x}^{2} - 49) \times \frac{1}{x - 7} = 10 \\ (x + 3)(x - 3) \times \frac{5}{x + 3} +(x + 7)(x - 7) \times \frac{1}{x - 7} = 10 \\ (x - 3) \times 5 + (x + 7) = 10 \\ 5x - 15 + x + 7 = 10 \\ 6x = 10 + 15 - 7 \\ 6x = 18 \\ x = 3[/tex]
