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Solve for y
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2xy+y=1-x^{2}
Subtract x^{2} from both sides.
\left(2x+1\right)y=1-x^{2}
Combine all terms containing y.
\frac{\left(2x+1\right)y}{2x+1}=\frac{1-x^{2}}{2x+1}
Divide both sides by 2x+1.
y=\frac{1-x^{2}}{2x+1}
Dividing by 2x+1 undoes the multiplication by 2x+1.