The function \(\displaystyle f(x) = \frac{2 \, x + 1}{x^{2} + 6 \, x + 5}\) has derivative \(\displaystyle f'(x) = \frac{-2 \, {\left(x + 2\right)} {\left(x - 1\right)}}{{\left(x + 5\right)}^{2} {\left(x + 1\right)}^{2}}\).
Don’t worry about finding the inflection point, the second derivative is not very nice and it doesn’t factor.