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\frac{2}{3}x-\frac{1}{2}y-\frac{1}{6}x
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.
\frac{1}{2}x-\frac{1}{2}y
Combine \frac{2}{3}x and -\frac{1}{6}x to get \frac{1}{2}x.
\frac{4x-3y-x}{6}
Factor out \frac{1}{6}.
3x-3y
Consider 4x-3y-x. Multiply and combine like terms.
3\left(x-y\right)
Consider 3x-3y. Factor out 3.
\frac{x-y}{2}
Rewrite the complete factored expression.