Solve frac{sqrt{3}-1}{sqrt{3}}

$$\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } }$$

Evaluate

$$-\frac{\sqrt{3}}{3}+1\approx 0.422649731$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{3}-1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(\sqrt{3}-1\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(\sqrt{3}-1\right)\sqrt{3}}{3}$$

Use the distributive property to multiply \sqrt{3}-1 by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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