Solve =frac{sqrt{2}+1}{sqrt{2}+1-1}

$$= \frac { \sqrt { 2 } + 1 } { \sqrt { 2 } + 1 - 1 }$$

Evaluate

$$\frac{\sqrt{2}}{2}+1\approx 1.707106781$$

Solution Steps

Subtract 1 from 1 to get 0.

$$\frac{\sqrt{2}+1}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{2}+1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{\left(\sqrt{2}+1\right)\sqrt{2}}{2}$$

Use the distributive property to multiply \sqrt{2}+1 by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{2+\sqrt{2}}{2}$$