Solve frac{1/sqrt{2}}{}+2/1-5/2

$$\frac{ \frac{ 1 }{ \sqrt{ 2 } } }{ } + \frac{ 2 }{ 1 } - \frac{ 5 }{ 2 }$$

Evaluate

$$\frac{\sqrt{2}-1}{2}\approx 0.207106781$$

Solution Steps

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

$$\frac{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{1}+\frac{2}{1}-\frac{5}{2}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{2}}{2}}{1}+\frac{2}{1}-\frac{5}{2}$$

Anything divided by one gives itself.

$$\frac{\sqrt{2}}{2}+\frac{2}{1}-\frac{5}{2}$$

Anything divided by one gives itself.

$$\frac{\sqrt{2}}{2}+2-\frac{5}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\sqrt{2}}{2}+\frac{4}{2}-\frac{5}{2}$$

Since \frac{4}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{2}}{2}+\frac{4-5}{2}$$

Subtract 5 from 4 to get -1.

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

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

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

Factor

$$\frac{\sqrt{2} - 1}{2} = 0.20710678118654757$$