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

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

Evaluate

$$\frac{\sqrt{3}}{3}+1\approx 1.577350269$$

Solution Steps

Subtract 1 from 1 to get 0.

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

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.

$$\frac{3+\sqrt{3}}{3}$$