Solve x^6y^3/2yx^2-2x^3y/3x

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

Factor

$$\frac{yx^{2}\left(3yx^{2}-4\right)}{6}$$

Solution Steps

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

$$factor(\frac{y^{2}x^{4}}{2}-\frac{2x^{3}y}{3x})$$

Cancel out x in both numerator and denominator.

$$factor(\frac{y^{2}x^{4}}{2}-\frac{2yx^{2}}{3})$$

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

$$factor(\frac{3y^{2}x^{4}}{6}-\frac{2\times 2yx^{2}}{6})$$

Since \frac{3y^{2}x^{4}}{6} and \frac{2\times 2yx^{2}}{6} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{3y^{2}x^{4}-2\times 2yx^{2}}{6})$$

Do the multiplications in 3y^{2}x^{4}-2\times 2yx^{2}.

$$factor(\frac{3y^{2}x^{4}-4yx^{2}}{6})$$

Consider 3y^{2}x^{4}-4yx^{2}. Factor out yx^{2}.

$$yx^{2}\left(3yx^{2}-4\right)$$

Rewrite the complete factored expression.

$$\frac{y\left(3yx^{2}-4\right)x^{2}}{6}$$

Evaluate

$$\frac{yx^{2}\left(3yx^{2}-4\right)}{6}$$