Verified answer

[tex]\displaystyle\bf\\y=\frac{x^{2}-6x }{x+4} \\\\\\y'=\frac{(x^{2} -6x)'\cdot (x+4)-(x^{2} -6x)\cdot(x+4)'}{(x+4)^{2} } =\\\\\\=\frac{(2x-6)\cdot (x+4)-(x^{2} -6x)\cdot 1}{(x+4)^{2} } =\frac{2x^{2} +8x-6x-24-x^{2} +6x}{(x+4)^{2} } =\\\\\\=\frac{x^{2} +8x-24}{(x+4)^{2} }[/tex]