Inverse Laplace Transform of $\frac{1}{s \left(\frac{s}{s + 1} + \frac{2}{2 s + 1}\right)}$

Find $\mathcal{L}^{-1}_{s}\left(\frac{1}{s \left(\frac{s}{s + 1} + \frac{2}{2 s + 1}\right)}\right)$.

The Inverse Laplace transform of $\frac{1}{s \left(\frac{s}{s + 1} + \frac{2}{2 s + 1}\right)}$A is $\frac{1}{2} + \frac{3 \sqrt{7} e^{- \frac{3 t}{4}} \sin{\left(\frac{\sqrt{7} t}{4} \right)}}{14} + \frac{e^{- \frac{3 t}{4}} \cos{\left(\frac{\sqrt{7} t}{4} \right)}}{2}$A.