laplace transform - Partial fraction for complex roots using the second order polynomial

$\frac{(s^2 +s +1)}{(s^2+4s+3)(s+1)}$

the answer has to be in a $\frac{A}{(s+1)} + \frac{Bs+C}{(s^2+4s+3)}$ form.
However i tried to solve it this way but end up with that there is no solution for this problem. For instance i get: $A=1+A$ to solve for A which is false. Please help me i spent a lot of time solving this question with different ways and have no ideas left.