Solve 1/2/frac{1{sqrt{2}}}+1/2-frac{frac{sqrt{3}}{2}}{1}-frac{frac{sqrt{3}}{2}}{1}

$$\frac { \frac { 1 } { 2 } } { \frac { 1 } { \sqrt { 2 } } } + \frac { 1 } { 2 } - \frac { \frac { \sqrt { 3 } } { 2 } } { 1 } - \frac { \frac { \sqrt { 3 } } { 2 } } { 1 }$$

Evaluate

$$\frac{\sqrt{2}+1-2\sqrt{3}}{2}\approx -0.524944026$$

Short Solution Steps

Divide \frac{1}{2} by \frac{1}{\sqrt{2}} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{\sqrt{2}}.

$$\frac{\sqrt{2}}{2}+\frac{1}{2}-\frac{\frac{\sqrt{3}}{2}}{1}-\frac{\frac{\sqrt{3}}{2}}{1}$$

Anything divided by one gives itself.

$$\frac{\sqrt{2}}{2}+\frac{1}{2}-\frac{\sqrt{3}}{2}-\frac{\frac{\sqrt{3}}{2}}{1}$$

Anything divided by one gives itself.

$$\frac{\sqrt{2}}{2}+\frac{1}{2}-\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2}$$

Combine -\frac{\sqrt{3}}{2} and -\frac{\sqrt{3}}{2} to get -\sqrt{3}.

$$\frac{\sqrt{2}}{2}+\frac{1}{2}-\sqrt{3}$$

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

$$\frac{\sqrt{2}+1}{2}-\sqrt{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3} times \frac{2}{2}.

$$\frac{\sqrt{2}+1}{2}-\frac{2\sqrt{3}}{2}$$

Since \frac{\sqrt{2}+1}{2} and \frac{2\sqrt{3}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{2}+1-2\sqrt{3}}{2}$$

Factor

$$\frac{\sqrt{2} + 1 - 2 \sqrt{3}}{2} = -0.5249440263823297$$