Solve for y
y=x-\frac{1}{x}
x\neq 0
Solve for x
x=\frac{\sqrt{y^{2}+4}+y}{2}
x=\frac{-\sqrt{y^{2}+4}+y}{2}
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-2xy=2-2x^{2}
Subtract 2x^{2} from both sides.
\left(-2x\right)y=2-2x^{2}
The equation is in standard form.
\frac{\left(-2x\right)y}{-2x}=\frac{2-2x^{2}}{-2x}
Divide both sides by -2x.
y=\frac{2-2x^{2}}{-2x}
Dividing by -2x undoes the multiplication by -2x.
y=x-\frac{1}{x}
Divide -2x^{2}+2 by -2x.
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