Solve -1/2x-3/4y^2+1/7x+1/3y^2

$$- \frac { 1 } { 2 } x - \frac { 3 } { 4 } y ^ { 2 } + \frac { 1 } { 7 } x + \frac { 1 } { 3 } y ^ { 2 }$$

Evaluate

$$-\frac{5y^{2}}{12}-\frac{5x}{14}$$

Solution Steps

Combine -\frac{1}{2}x and \frac{1}{7}x to get -\frac{5}{14}x.

$$-\frac{5}{14}x-\frac{3}{4}y^{2}+\frac{1}{3}y^{2}$$

Combine -\frac{3}{4}y^{2} and \frac{1}{3}y^{2} to get -\frac{5}{12}y^{2}.

$$-\frac{5}{14}x-\frac{5}{12}y^{2}$$

Factor

$$\frac{5\left(-6x-7y^{2}\right)}{84}$$

Solution Steps

Factor out \frac{1}{84}.

$$\frac{-42x-63y^{2}+12x+28y^{2}}{84}$$

Consider -42x-63y^{2}+12x+28y^{2}. Multiply and combine like terms.

$$-30x-35y^{2}$$

Consider -30x-35y^{2}. Factor out 5.

$$5\left(-6x-7y^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{5\left(-6x-7y^{2}\right)}{84}$$