Why only the numerator is derived? Why the derivative of $y = \frac{x^5}{a+b}-\frac{x^2}{a-b}-x$ is solved by deriving just the numerators?
The solution is $\frac{dy}{dx}=\frac{5x^4}{a-b}-\frac{2x}{a-b}-1$.

Because the denominator does not depend on $x$. So if we were to formally use $\left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v^2}$ we get by plugging $v'=0$ ($v$ does not depend on $x$) $\left(\frac{u}{v}\right)'=\frac{u'}{v}$
