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2xy-2x+4y=0
Swap sides so that all variable terms are on the left hand side.
2xy-2x=-4y
Subtract 4y from both sides. Anything subtracted from zero gives its negation.
\left(2y-2\right)x=-4y
Combine all terms containing x.
\frac{\left(2y-2\right)x}{2y-2}=-\frac{4y}{2y-2}
Divide both sides by 2y-2.
x=-\frac{4y}{2y-2}
Dividing by 2y-2 undoes the multiplication by 2y-2.
x=-\frac{2y}{y-1}
Divide -4y by 2y-2.
2xy-2x+4y=0
Swap sides so that all variable terms are on the left hand side.
2xy+4y=2x
Add 2x to both sides. Anything plus zero gives itself.
\left(2x+4\right)y=2x
Combine all terms containing y.
\frac{\left(2x+4\right)y}{2x+4}=\frac{2x}{2x+4}
Divide both sides by 2x+4.
y=\frac{2x}{2x+4}
Dividing by 2x+4 undoes the multiplication by 2x+4.
y=\frac{x}{x+2}
Divide 2x by 2x+4.