Solve for y
y=2+\frac{1}{x^{2}}
x\neq 0
Solve for x (complex solution)
x=-\left(y-2\right)^{-\frac{1}{2}}
x=\left(y-2\right)^{-\frac{1}{2}}\text{, }y\neq 2
Solve for x
x=\frac{1}{\sqrt{y-2}}
x=-\frac{1}{\sqrt{y-2}}\text{, }y>2
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2x^{2}y=2+4x^{2}
Add 4x^{2} to both sides.
2x^{2}y=4x^{2}+2
The equation is in standard form.
\frac{2x^{2}y}{2x^{2}}=\frac{4x^{2}+2}{2x^{2}}
Divide both sides by 2x^{2}.
y=\frac{4x^{2}+2}{2x^{2}}
Dividing by 2x^{2} undoes the multiplication by 2x^{2}.
y=2+\frac{1}{x^{2}}
Divide 2+4x^{2} by 2x^{2}.
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