Løs for x (complex solution)
\left\{\begin{matrix}\\x=\frac{-\sqrt{\left(y-1\right)\left(y+3\right)}+y-1}{2}\text{, }&\text{unconditionally}\\x=\frac{\sqrt{\left(y-1\right)\left(y+3\right)}+y-1}{2}\text{, }&y\neq \frac{3}{2}\end{matrix}\right,
Løs for y (complex solution)
y=\frac{x^{2}+x+1}{x+1}
x\neq -1\text{ and }x\neq 1
Løs for x
\left\{\begin{matrix}x=\frac{\sqrt{\left(y-1\right)\left(y+3\right)}+y-1}{2}\text{, }&y\leq -3\text{ or }\left(y\neq \frac{3}{2}\text{ and }y\geq 1\right)\\x=\frac{-\sqrt{\left(y-1\right)\left(y+3\right)}+y-1}{2}\text{, }&y\leq -3\text{ or }y\geq 1\end{matrix}\right,
Løs for y
y=\frac{x^{2}+x+1}{x+1}
|x|\neq 1
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