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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Factor

$$\frac{x\left(-14y-3\right)}{14}$$

Solution Steps

Factor out \frac{1}{56}.

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

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

$$-56xy-12x$$

Consider -56xy-12x. Factor out 4.

$$4\left(-14xy-3x\right)$$

Consider -14xy-3x. Factor out x.

$$x\left(-14y-3\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(-14y-3\right)}{14}$$