Solve 2/3x+3/4y-x-y+1/6x-2/9y

$$\frac{ 2 }{ 3 } x+ \frac{ 3 }{ 4 } y-x-y+ \frac{ 1 }{ 6 } x- \frac{ 2 }{ 9 } y$$

Evaluate

$$-\frac{x}{6}-\frac{17y}{36}$$

Solution Steps

Combine \frac{2}{3}x and -x to get -\frac{1}{3}x.

$$-\frac{1}{3}x+\frac{3}{4}y-y+\frac{1}{6}x-\frac{2}{9}y$$

Combine \frac{3}{4}y and -y to get -\frac{1}{4}y.

$$-\frac{1}{3}x-\frac{1}{4}y+\frac{1}{6}x-\frac{2}{9}y$$

Combine -\frac{1}{3}x and \frac{1}{6}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x-\frac{1}{4}y-\frac{2}{9}y$$

Combine -\frac{1}{4}y and -\frac{2}{9}y to get -\frac{17}{36}y.

$$-\frac{1}{6}x-\frac{17}{36}y$$

Factor

$$\frac{-6x-17y}{36}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{24x+27y-36x-36y+6x-8y}{36}$$

Consider 24x+27y-36x-36y+6x-8y. Multiply and combine like terms.

$$-6x-17y$$

Rewrite the complete factored expression.

$$\frac{-6x-17y}{36}$$