Solve sqrt{2}+1-frac{sqrt{2}(sqrt{2}+1)}{2}

$$\sqrt { 2 } + 1 - \frac { \sqrt { 2 } ( \sqrt { 2 } + 1 ) } { 2 }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{2}+1 times \frac{2}{2}.

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

Since \frac{2\left(\sqrt{2}+1\right)}{2} and \frac{\sqrt{2}\left(\sqrt{2}+1\right)}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\left(\sqrt{2}+1\right)-\sqrt{2}\left(\sqrt{2}+1\right).

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

Do the calculations in 2\sqrt{2}+2-2-\sqrt{2}.

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