Answer
$x = 7, -1$
Work Step by Step
$\frac{x-2}{x-5} = \frac{2x+1}{x-1}$
$(x-1)(x-2) = (2x+1)(x-5)$
$x(x-1)-2(x-1) = x(2x+1)-5(2x+1)$
$x^{2}-x -2x +2 = 2x^{2} + x - 10x -5$
$x^{2} -3x + 2 = 2x^{2} -9x - 5$
$2x^{2} -9x - 5= x^{2} -3x + 2$
$x^{2} -6x - 7 = 0$
$(x-7)(x+1) = 0$
$x = 7, -1$
