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-\frac{1}{6}xy+\frac{3}{4}x^{2}-y^{2}-\frac{1}{2}x^{2}
Combine -\frac{2}{3}xy and \frac{1}{2}xy to get -\frac{1}{6}xy.
-\frac{1}{6}xy+\frac{1}{4}x^{2}-y^{2}
Combine \frac{3}{4}x^{2} and -\frac{1}{2}x^{2} to get \frac{1}{4}x^{2}.
\frac{-8xy+9x^{2}-12y^{2}+6xy-6x^{2}}{12}
Factor out \frac{1}{12}.