Question

3/x-2 - 2/x-3 = 4/x-3 - 3/x-1​

Answer 1

Step-by-step explanation:

$\frac{3}{x - 2} - \frac{2}{x - 3} = \frac{4}{x - 3} - \frac{3}{x - 1} \\ \frac{3}{x - 1} + \frac{3}{x - 2} = \frac{4}{x - 3} + \frac{2}{x -3 } \\ \frac{3(x - 2) + 3(x - 1)}{(x - 2)(x - 1)} = \frac{6}{x - 3} \\ \frac{3x - 6 + 3x - 3}{ {x}^{2} - x - 2x + 2} = \frac{6}{x - 3} \\ \frac{6x - 9}{ {x}^{2} - 3x + 2} = \frac{6}{x - 3} \\ (6x - 9)(x - 3) = 6( {x}^{2} - 3x + 2) \\ 6 {x}^{2} - 18x - 9x + 27 = 6 {x}^{2} - 18x + 12 \\ - 9x = 12 - 27 \\ - 9x = - 15 \\ x = \frac{15}{9} = \frac{5}{3} \: answer$