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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x^{3} and 3x^{2} is 6x^{3}. Multiply \frac{2xy-1}{2x^{3}} times \frac{3}{3}. Multiply \frac{3y+4}{3x^{2}} times \frac{2x}{2x}.

$$\frac{3\left(2xy-1\right)}{6x^{3}}-\frac{\left(3y+4\right)\times 2x}{6x^{3}}$$

Since \frac{3\left(2xy-1\right)}{6x^{3}} and \frac{\left(3y+4\right)\times 2x}{6x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(2xy-1\right)-\left(3y+4\right)\times 2x}{6x^{3}}$$

Do the multiplications in 3\left(2xy-1\right)-\left(3y+4\right)\times 2x.

$$\frac{6xy-3-6yx-8x}{6x^{3}}$$

Combine like terms in 6xy-3-6yx-8x.

$$\frac{-3-8x}{6x^{3}}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x^{3} and 3x^{2} is 6x^{3}. Multiply \frac{2xy-1}{2x^{3}} times \frac{3}{3}. Multiply \frac{3y+4}{3x^{2}} times \frac{2x}{2x}.

$$\frac{3\left(2xy-1\right)}{6x^{3}}-\frac{\left(3y+4\right)\times 2x}{6x^{3}}$$

Since \frac{3\left(2xy-1\right)}{6x^{3}} and \frac{\left(3y+4\right)\times 2x}{6x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(2xy-1\right)-\left(3y+4\right)\times 2x}{6x^{3}}$$

Do the multiplications in 3\left(2xy-1\right)-\left(3y+4\right)\times 2x.

$$\frac{6xy-3-6yx-8x}{6x^{3}}$$

Combine like terms in 6xy-3-6yx-8x.

$$\frac{-3-8x}{6x^{3}}$$