Solve 3/2/sqrt{2/2}-frac{5/3}{frac{sqrt{2}}{2}}

$$\frac { \frac { 3 } { 2 } } { \frac { \sqrt { 2 } } { 2 } } - \frac { \frac { 5 } { 3 } } { \frac { \sqrt { 2 } } { 2 } }$$

Evaluate

$$-\frac{\sqrt{2}}{6}\approx -0.23570226$$

Solution Steps

Divide \frac{3}{2} by \frac{\sqrt{2}}{2} by multiplying \frac{3}{2} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{3\times 2}{2\sqrt{2}}-\frac{\frac{5}{3}}{\frac{\sqrt{2}}{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{\sqrt{2}}-\frac{\frac{5}{3}}{\frac{\sqrt{2}}{2}}$$

Rationalize the denominator of \frac{3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{\frac{5}{3}}{\frac{\sqrt{2}}{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2}-\frac{\frac{5}{3}}{\frac{\sqrt{2}}{2}}$$

Divide \frac{5}{3} by \frac{\sqrt{2}}{2} by multiplying \frac{5}{3} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{3\sqrt{2}}{2}-\frac{5\times 2}{3\sqrt{2}}$$

Multiply 5 and 2 to get 10.

$$\frac{3\sqrt{2}}{2}-\frac{10}{3\sqrt{2}}$$

Rationalize the denominator of \frac{10}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{2}-\frac{10\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2}-\frac{10\sqrt{2}}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{2}}{2}-\frac{5\sqrt{2}}{3}$$

Combine \frac{3\sqrt{2}}{2} and -\frac{5\sqrt{2}}{3} to get -\frac{1}{6}\sqrt{2}.

$$-\frac{1}{6}\sqrt{2}$$