Solve (-3/4xy+2/7x+1/8y)+(1/2y-frac{1}{2}x-xy)-frac{5}{8}y

$$( - \frac { 3 } { 4 } x y + \frac { 2 } { 7 } x + \frac { 1 } { 8 } y ) + ( \frac { 1 } { 2 } y - \frac { 1 } { 2 } x - x y ) - \frac { 5 } { 8 } y$$

Evaluate

$$-\frac{7xy}{4}-\frac{3x}{14}$$

Solution Steps

Combine \frac{1}{8}y and \frac{1}{2}y to get \frac{5}{8}y.

$$-\frac{3}{4}xy+\frac{2}{7}x+\frac{5}{8}y-\frac{1}{2}x-xy-\frac{5}{8}y$$

Combine \frac{2}{7}x and -\frac{1}{2}x to get -\frac{3}{14}x.

$$-\frac{3}{4}xy-\frac{3}{14}x+\frac{5}{8}y-xy-\frac{5}{8}y$$

Combine -\frac{3}{4}xy and -xy to get -\frac{7}{4}xy.

$$-\frac{7}{4}xy-\frac{3}{14}x+\frac{5}{8}y-\frac{5}{8}y$$

Combine \frac{5}{8}y and -\frac{5}{8}y to get 0.

$$-\frac{7}{4}xy-\frac{3}{14}x$$

Factor

$$\frac{x\left(-49y-6\right)}{28}$$

Solution Steps

Factor out \frac{1}{56}.

$$\frac{-42xy+16x+7y+28y-28x-56xy-35y}{56}$$

Consider -42xy+16x+7y+28y-28x-56xy-35y. Multiply and combine like terms.

$$-98xy-12x$$

Consider -98xy-12x. Factor out 2.

$$2\left(-49xy-6x\right)$$

Consider -49xy-6x. Factor out x.

$$x\left(-49y-6\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(-49y-6\right)}{28}$$