Solve 2/3x^2y-1/4xy^2-3x-y/6x^2y^2=

$$\frac { 2 } { 3 x ^ { 2 } y } - \frac { 1 } { 4 x y ^ { 2 } } - \frac { 3 x - y } { 6 x ^ { 2 } y ^ { 2 } } =$$

Evaluate

$$\frac{10y-9x}{12\left(xy\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{2}y and 4xy^{2} is 12x^{2}y^{2}. Multiply \frac{2}{3x^{2}y} times \frac{4y}{4y}. Multiply \frac{1}{4xy^{2}} times \frac{3x}{3x}.

$$\frac{2\times 4y}{12x^{2}y^{2}}-\frac{3x}{12x^{2}y^{2}}-\frac{3x-y}{6x^{2}y^{2}}$$

Since \frac{2\times 4y}{12x^{2}y^{2}} and \frac{3x}{12x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 4y-3x}{12x^{2}y^{2}}-\frac{3x-y}{6x^{2}y^{2}}$$

Do the multiplications in 2\times 4y-3x.

$$\frac{8y-3x}{12x^{2}y^{2}}-\frac{3x-y}{6x^{2}y^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12x^{2}y^{2} and 6x^{2}y^{2} is 12x^{2}y^{2}. Multiply \frac{3x-y}{6x^{2}y^{2}} times \frac{2}{2}.

$$\frac{8y-3x}{12x^{2}y^{2}}-\frac{2\left(3x-y\right)}{12x^{2}y^{2}}$$

Since \frac{8y-3x}{12x^{2}y^{2}} and \frac{2\left(3x-y\right)}{12x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8y-3x-2\left(3x-y\right)}{12x^{2}y^{2}}$$

Do the multiplications in 8y-3x-2\left(3x-y\right).

$$\frac{8y-3x-6x+2y}{12x^{2}y^{2}}$$

Combine like terms in 8y-3x-6x+2y.

$$\frac{10y-9x}{12x^{2}y^{2}}$$

Expand

$$\frac{10y-9x}{12\left(xy\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{2}y and 4xy^{2} is 12x^{2}y^{2}. Multiply \frac{2}{3x^{2}y} times \frac{4y}{4y}. Multiply \frac{1}{4xy^{2}} times \frac{3x}{3x}.

$$\frac{2\times 4y}{12x^{2}y^{2}}-\frac{3x}{12x^{2}y^{2}}-\frac{3x-y}{6x^{2}y^{2}}$$

Since \frac{2\times 4y}{12x^{2}y^{2}} and \frac{3x}{12x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 4y-3x}{12x^{2}y^{2}}-\frac{3x-y}{6x^{2}y^{2}}$$

Do the multiplications in 2\times 4y-3x.

$$\frac{8y-3x}{12x^{2}y^{2}}-\frac{3x-y}{6x^{2}y^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12x^{2}y^{2} and 6x^{2}y^{2} is 12x^{2}y^{2}. Multiply \frac{3x-y}{6x^{2}y^{2}} times \frac{2}{2}.

$$\frac{8y-3x}{12x^{2}y^{2}}-\frac{2\left(3x-y\right)}{12x^{2}y^{2}}$$

Since \frac{8y-3x}{12x^{2}y^{2}} and \frac{2\left(3x-y\right)}{12x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8y-3x-2\left(3x-y\right)}{12x^{2}y^{2}}$$

Do the multiplications in 8y-3x-2\left(3x-y\right).

$$\frac{8y-3x-6x+2y}{12x^{2}y^{2}}$$

Combine like terms in 8y-3x-6x+2y.

$$\frac{10y-9x}{12x^{2}y^{2}}$$