Solve f:frac{2sqrt{3}}{sqrt{2}}=1/2

$$f : \frac { 2 \sqrt { 3 } } { \sqrt { 2 } } = \frac { 1 } { 2 }$$

Solve for f

$$f = \frac{\sqrt{6}}{2} \approx 1.224744871$$

Steps for Solving Linear Equation

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

$$\frac{f\sqrt{2}}{2\sqrt{3}}=\frac{1}{2}$$

Factor the expressions that are not already factored in \frac{f\sqrt{2}}{2\sqrt{3}}.

$$\frac{\sqrt{2}f}{2\sqrt{3}}=\frac{1}{2}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{f}{\sqrt{2}\sqrt{3}}=\frac{1}{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{f}{\sqrt{6}}=\frac{1}{2}$$

Rationalize the denominator of \frac{f}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{f\sqrt{6}}{\left(\sqrt{6}\right)^{2}}=\frac{1}{2}$$

The square of \sqrt{6} is 6.

$$\frac{f\sqrt{6}}{6}=\frac{1}{2}$$

Multiply both sides by 6.

$$f\sqrt{6}=\frac{1}{2}\times 6$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$f\sqrt{6}=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$f\sqrt{6}=3$$

The equation is in standard form.

$$\sqrt{6}f=3$$

Divide both sides by \sqrt{6}.

$$\frac{\sqrt{6}f}{\sqrt{6}}=\frac{3}{\sqrt{6}}$$

Dividing by \sqrt{6} undoes the multiplication by \sqrt{6}.

$$f=\frac{3}{\sqrt{6}}$$

Divide 3 by \sqrt{6}.

$$f=\frac{\sqrt{6}}{2}$$