Question

\frac{4}{x - 3} - \frac{3}{x - 1 } = \frac{5}{x - 1} - \frac{4}{x - 2}​

Answer 1

$\frac{4}{x - 3} - \frac{3}{x - 1 } = \frac{5}{x - 1} - \frac{4}{x - 2}\\\frac{4x - 4 - 3x + 3}{x^2 - 4x + 3} = \frac{5x - 10 - 4x + 4}{x^2 - 3x + 2}\\\frac{x-1}{x^2 - 4x - 3} = \frac{x-6}{x^2 - 3x - 2}\\(x-1) ( x^2 - 3x - 2) = (x-6)(x^2-4x-3)\\x^3 - 3x^2 - 2x - x^2 + 3x + 2 = x^3 - 4x^2 - 3x - 6x^2 + 24x + 18\\-4x^2 + x + 2 = -10x^2 + 21x + 18\\6x^2 + 2 = 20x + 18\\6x^2 - 20x = 16\\6x^2 - 20x - 16 = 0\\6x^2 -24x + 4x - 16 = 0 =6x(x - 4) + 4(x - 4) = 0 = (x -4)(6x + 4) = 0\\x\ = 4\ or\ x = -2/3$

Answer 2

your answer is in the attachment hope it will helps you