Question

4/x-3 - 3/x-1 = 5/x-1 - 4/x-2​

Answer 1

$\frac{4}{x - 3} - \frac{3}{x - 1} = \frac{5}{x - 1} - \frac{4}{x - 2} \\ \\ \frac{4}{x - 3} + \frac{4}{x - 2} = \frac{5}{x - 1} + \frac{3}{x - 1} \\ \\ 4( \frac{x - 2 + x - 3}{ {x}^{2} - 5x + 6} ) = \frac{8}{x - 1} \\ \\ 8 {x}^{2} - 40x + 48 = (8x - 20)(x - 1) \\ \\ 8 {x}^{2} - 40x + 48 = 8 {x}^{2} - 28x + 20 \\ \\ -12x = -28 \\ \\ x = \frac{28}{12} \\ \\ x= \frac{7}{3}$