[tex]m^2x+mx+m+1 = 0 \Rightarrow x(m^2+m)+m+1 = 0 \Rightarrow \\ \\ \Rightarrow (m^2+m)x = -(m+1) \Rightarrow x = -\frac{m+1}{m^2+m}\Rightarrow \\ \\ \Rightarrow x = - \frac{m+1}{m(m+1)} \Rightarrow x = -\frac{1}{m}, \quad \forall m\in \mathbb_{R}^*[/tex]