Example 5. Solve the equation $\mathbf{x}^{2}+\mathbf{x}+1=\frac{\mathbf{2}}{\mathbf{x}^{2}+\mathbf{x}}$ (Page 125, 5.(3))
Solve the original equation $\stackrel{\text { transformation }}{\Longleftrightarrow} x^{2}+x-\frac{2}{x^{2}+x}=-1$ <Proposition 1> $x^{2}+x=1$ or $x^{2}+x=-2$ (no solution), solving it yields $x_{1}=$ $\frac{-1+\sqrt{5}}{2}, x_{2}=\frac{-1-\sqrt{5}}{2}$ as the roots of the original equation.