Answer
Since $x \ne -1$, there is no solution.
Work Step by Step
$\ln (x-5) - \ln (x+4) = \ln (x-1) - \ln (x+2)$
$\ln \frac{x-5}{x+4} = \ln \frac{x-1}{x+2}$
$ \frac{x-5}{x+4} = \frac{x-1}{x+2}$
$(x-5)(x+2) = (x-1)(x+4)$
$x(x+2)-5(x+2) = x(x+4)-1(x+4)$
$x^{2} + 2x - 5x - 10 = x^{2} + 4x - x - 4$
$x^{2} - 3x - 10 = x^{2} + 3x - 4$
$x^{2} - x^{2} - 3x - 3x - 10 + 4 = 0$
$-6x - 6 = 0 $
$-6x = 6$
$x = -1$
Since $x \ne -1$, there is no solution.
