( x ) = \lim ( x + 1 - \sqrt { x ^ { 2 } + 2 } ) =
Solve for l
\left\{\begin{matrix}l=\frac{x}{-Im(\sqrt{x^{2}+2})+Im(x)}\text{, }&-Im(\sqrt{x^{2}+2})+Im(x)\neq 0\\l\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
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lIm(x+1-\sqrt{x^{2}+2})=x
Swap sides so that all variable terms are on the left hand side.
\left(-Im(\sqrt{x^{2}+2})+Im(x)\right)l=x
The equation is in standard form.
\frac{\left(-Im(\sqrt{x^{2}+2})+Im(x)\right)l}{-Im(\sqrt{x^{2}+2})+Im(x)}=\frac{x}{-Im(\sqrt{x^{2}+2})+Im(x)}
Divide both sides by Im(x)-Im(\sqrt{x^{2}+2}).
l=\frac{x}{-Im(\sqrt{x^{2}+2})+Im(x)}
Dividing by Im(x)-Im(\sqrt{x^{2}+2}) undoes the multiplication by Im(x)-Im(\sqrt{x^{2}+2}).
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