Solve frac{sqrt{3}x^3}{4}-frac{sqrt{2}x^4}{2}

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

Evaluate

$$\frac{\left(-2\sqrt{2}x+\sqrt{3}\right)x^{3}}{4}$$

Short Solution Steps

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

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

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

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

Factor

$$\frac{\left(-2\sqrt{2}x+\sqrt{3}\right)x^{3}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

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

Consider \sqrt{3}x^{3}-2\sqrt{2}x^{4}. Factor out x^{3}.

$$x^{3}\left(\sqrt{3}-2\sqrt{2}x\right)$$

Rewrite the complete factored expression.

$$\frac{x^{3}\left(\sqrt{3}-2\sqrt{2}x\right)}{4}$$