Question

answer this question.its coming in my test.the answered should be 5 /3​

Answer 1

Answer:

$x = \frac{5}{3}$

Step-by-step explanation:

$\frac{3}{x - 2} - \frac{2}{x - 3} = \frac{4}{x - 3} - \frac{3}{x - 1} \\ \frac{3}{x - 2} + \frac{3}{x - 1} = \frac{4}{x - 3} + \frac{2}{x - 3} \\ \frac{3(x - 1) + 3(x - 2)}{(x - 2)(x - 1)} = \frac{4 + 2}{x - 3} \\ \frac{3x - 3 + 3x - 6}{x(x - 1) - 2(x - 1)} = \frac{6}{x - 3} \\ \frac{3x + 3x - 3 - 6}{ {x}^{2} - x - 2x + 2} = \frac{6}{x - 3} \\ \frac{6x - 9}{ {x}^{2} - 3x + 2 } = \frac{6}{x - 3} \\cross\: multiply \\ 6 ({x}^{2} - 3x + 2) = (x - 3)(6x - 9) \\ 6 {x}^{2} - 18x + 12 = x(6x - 9) - 3(6x - 9) \\ 6 {x}^{2} - 18x + 12 = 6 {x}^{2} - 9x - 18x + 27 \\ 6 {x}^{2} - 6 {x}^{2} - 18x + 18x + 9x + 12 - 27 = 0 \\ 9x - 15 = 0 \\ 9x = 15 \\ x = \frac{15}{9} = \frac{5}{3}$