$ \frac{x-2}{x+3} = \frac{x+4}{x-5} \rightarrow (x-2)(x-5) = (x+4)(x+3) \\ x^2-7x+10 = x^2+7x+12 \Rightarrow -2=14x \Rightarrow x = \frac{-2}{14}=- \frac{1}{7}  $