Solve 2xy+5/14x^{5}y^{3}z:(2/7x^3y^3z)-9/2x^4:(3x^2)-xy

$$2 x y + \frac { 5 } { 14 } x ^ { 5 } y ^ { 3 } z : ( \frac { 2 } { 7 } x ^ { 3 } y ^ { 3 } z ) - \frac { 9 } { 2 } x ^ { 4 } : ( 3 x ^ { 2 } ) - x y$$

Evaluate

$$xy-\frac{x^{2}}{4}$$

Solution Steps

Cancel out zx^{3}y^{3} in both numerator and denominator.

$$2xy+\frac{\frac{5}{14}x^{2}}{\frac{2}{7}}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy$$

Divide \frac{5}{14}x^{2} by \frac{2}{7} by multiplying \frac{5}{14}x^{2} by the reciprocal of \frac{2}{7}.

$$2xy+\frac{\frac{5}{14}x^{2}\times 7}{2}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy$$

Multiply \frac{5}{14} and 7 to get \frac{5}{2}.

$$2xy+\frac{\frac{5}{2}x^{2}}{2}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy$$

Divide \frac{5}{2}x^{2} by 2 to get \frac{5}{4}x^{2}.

$$2xy+\frac{5}{4}x^{2}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy$$

Cancel out x^{2} in both numerator and denominator.

$$2xy+\frac{5}{4}x^{2}-\frac{\frac{9}{2}x^{2}}{3}-xy$$

Divide \frac{9}{2}x^{2} by 3 to get \frac{3}{2}x^{2}.

$$2xy+\frac{5}{4}x^{2}-\frac{3}{2}x^{2}-xy$$

Combine 2xy and -xy to get xy.

$$xy+\frac{5}{4}x^{2}-\frac{3}{2}x^{2}$$

Combine \frac{5}{4}x^{2} and -\frac{3}{2}x^{2} to get -\frac{1}{4}x^{2}.

$$xy-\frac{1}{4}x^{2}$$

Factor

$$\frac{x\left(4y-x\right)}{4}$$

Solution Steps

Cancel out zx^{3}y^{3} in both numerator and denominator.

$$factor(2xy+\frac{\frac{5}{14}x^{2}}{\frac{2}{7}}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy)$$

Divide \frac{5}{14}x^{2} by \frac{2}{7} by multiplying \frac{5}{14}x^{2} by the reciprocal of \frac{2}{7}.

$$factor(2xy+\frac{\frac{5}{14}x^{2}\times 7}{2}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy)$$

Multiply \frac{5}{14} and 7 to get \frac{5}{2}.

$$factor(2xy+\frac{\frac{5}{2}x^{2}}{2}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy)$$

Divide \frac{5}{2}x^{2} by 2 to get \frac{5}{4}x^{2}.

$$factor(2xy+\frac{5}{4}x^{2}-\frac{\frac{9}{2}x^{4}}{3x^{2}}-xy)$$

Cancel out x^{2} in both numerator and denominator.

$$factor(2xy+\frac{5}{4}x^{2}-\frac{\frac{9}{2}x^{2}}{3}-xy)$$

Divide \frac{9}{2}x^{2} by 3 to get \frac{3}{2}x^{2}.

$$factor(2xy+\frac{5}{4}x^{2}-\frac{3}{2}x^{2}-xy)$$

Combine 2xy and -xy to get xy.

$$factor(xy+\frac{5}{4}x^{2}-\frac{3}{2}x^{2})$$

Combine \frac{5}{4}x^{2} and -\frac{3}{2}x^{2} to get -\frac{1}{4}x^{2}.

$$factor(xy-\frac{1}{4}x^{2})$$

Factor out \frac{1}{4}.

$$\frac{4xy-x^{2}}{4}$$

Consider 4xy-x^{2}. Factor out x.

$$x\left(4y-x\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(-x+4y\right)}{4}$$