Question

Apply the properties and simplify the expressions 1/2+3/4 and -5/6x + 1/3 xy - 3y

Answer 1

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