Solve xsqrt{3}-50/sqrt{3}

$$x \sqrt { 3 } - \frac { 50 } { \sqrt { 3 } }$$

Evaluate

$$\frac{\sqrt{3}\left(3x-50\right)}{3}$$

Short Solution Steps

Rationalize the denominator of \frac{50}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$x\sqrt{3}-\frac{50\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$x\sqrt{3}-\frac{50\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x\sqrt{3} times \frac{3}{3}.

$$\frac{3x\sqrt{3}}{3}-\frac{50\sqrt{3}}{3}$$

Since \frac{3x\sqrt{3}}{3} and \frac{50\sqrt{3}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x\sqrt{3}-50\sqrt{3}}{3}$$

Factor

$$\frac{\sqrt{3}\left(3x-50\right)}{3}$$

Solution Steps

Rationalize the denominator of \frac{50}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$factor(x\sqrt{3}-\frac{50\sqrt{3}}{\left(\sqrt{3}\right)^{2}})$$

The square of \sqrt{3} is 3.

$$factor(x\sqrt{3}-\frac{50\sqrt{3}}{3})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x\sqrt{3} times \frac{3}{3}.

$$factor(\frac{3x\sqrt{3}}{3}-\frac{50\sqrt{3}}{3})$$

Since \frac{3x\sqrt{3}}{3} and \frac{50\sqrt{3}}{3} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{3x\sqrt{3}-50\sqrt{3}}{3})$$

Consider 3x\sqrt{3}-50\sqrt{3}. Factor out \sqrt{3}.

$$\sqrt{3}\left(\sqrt{3}x\sqrt{3}-50\right)$$

Rewrite the complete factored expression.

$$\frac{\left(3x-50\right)\sqrt{3}}{3}$$