[tex]\begin{gathered} -\frac{1}{2}x+\frac{3}{4}xy+\frac{2}{3}y-\frac{5}{6}x+\frac{1}{3}xy-3y \\ \\ \\ =-\frac{1}{2}x+\frac{3}{4}xy+\frac{2}{3}y-\frac{5}{6}x+\frac{1}{3}xy-3y \\ \\ \text{Combine like terms:} \\ \\ =(-\frac{1}{2}x-\frac{5}{6}x)+(\frac{3}{4}xy+\frac{1}{3}xy)+(\frac{2}{3}y-3y) \\ \\ \text{Addition or substraction of fractions:} \\ \frac{a}{b}\pm\frac{c}{d}=\frac{ad\pm bc}{bd} \\ \\ \\ =\frac{-6x-10x}{12}+\frac{9xy+4xy}{12}+\frac{2y-9y}{3} \\ \\ =-\frac{16}{12}x+\frac{13}{12}xy-\frac{7}{3}y \\ \\ Simplify\colon \\ =-\frac{4}{3}x+\frac{13}{12}xy-\frac{7}{3}y \\ \end{gathered}[/tex]
