Solve x/2y+3y/x^2)^3

$$\frac { x } { 2 y } + \frac { 3 y } { x ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{x}{2y}+\frac{3y}{x^{2}}$$

Short Solution Steps

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

$$\frac{xx^{2}}{2yx^{2}}+\frac{3y\times 2y}{2yx^{2}}$$

Since \frac{xx^{2}}{2yx^{2}} and \frac{3y\times 2y}{2yx^{2}} have the same denominator, add them by adding their numerators.

$$\frac{xx^{2}+3y\times 2y}{2yx^{2}}$$

Do the multiplications in xx^{2}+3y\times 2y.

$$\frac{x^{3}+6y^{2}}{2yx^{2}}$$

Factor

$$\frac{x^{3}+6y^{2}}{2yx^{2}}$$