solve the equation in $\Bbb C $ \begin{array}{l}{\text {Solve in } \mathbb{C}}: \\ {x^{2}+\left(\frac{x}{x+1}\right)^{2}=3} \\ {\text { my try: }} \\ {x^{2}(x+1)^{2}+x^{2}=3(x+1)^{2}} \\ {x^{2}\left(x^{2}+2 x+1\right)-3\left(x^{2}+2 x+1\right)+x^{2}=0} \\ ({x^{2}-3 )\left(x^{2}+2 x+1\right)+x^{2}=0} \\ {x^{4}+2 x^{3}-x^{2}-6 x-3=0} \\ {\text { Now what should I do? }}\end{array}

An easier solution than expanding like you did:
$$x^2+\left(\frac{x}{x+1}\right)^2=3$$
$$\left(x-\frac{x}{x+1}\right)^2+\frac{2x^2}{x+1}=3$$
Put $\frac{x^2}{x+1}=t$. Then, $t^2+2t=3$. So, $t=1$ or $t=-3$.
This gives that either $x^2-x-1=0$ or $x^2+3x+3=0$ which can be solved easily.
