Answer
$\color{blue}{\dfrac{x-4}{x-5}}$
Work Step by Step
$\require{cancel}
\\=\dfrac{(x+5)(x-3)}{(x+5)(x+6)} \cdot \dfrac{(x+6)(x-4)}{(x-5)(x-3)}
\\=\dfrac{\cancel{(x+5)}\cancel{(x-3)}}{\cancel{(x+5)}\cancel{(x+6)}} \cdot \dfrac{c\cancel{(x+6)}(x-4)}{(x-5)\cancel{(x-3)}}
\\=\color{blue}{\dfrac{x-4}{x-5}}$
