Solve frac{sqrt{3}}{x}(3sqrt{2}-sqrt{10})

$$\frac { \sqrt { 3 } } { x } ( 3 \sqrt { 2 } - \sqrt { 10 } )$$

Evaluate

$$\frac{3\sqrt{6}-\sqrt{30}}{x}$$

Solution Steps

Express \frac{\sqrt{3}}{x}\left(3\sqrt{2}-\sqrt{10}\right) as a single fraction.

$$\frac{\sqrt{3}\left(3\sqrt{2}-\sqrt{10}\right)}{x}$$

Use the distributive property to multiply \sqrt{3} by 3\sqrt{2}-\sqrt{10}.

$$\frac{3\sqrt{3}\sqrt{2}-\sqrt{3}\sqrt{10}}{x}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{6}-\sqrt{3}\sqrt{10}}{x}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{3\sqrt{6}-\sqrt{30}}{x}$$

Differentiate w.r.t. x

$$\frac{\sqrt{30}-3\sqrt{6}}{x^{2}}$$