Solve DC=frac{1/2*sqrt{2}}{sqrt{3}}

$$D C = \frac { \frac { 1 } { 2 } \times \sqrt { 2 } } { \sqrt { 3 } }$$

Solve for C

$$C=\frac{\sqrt{6}}{6D}$$

$$D\neq 0$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\frac{1}{2}\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$DC=\frac{\frac{1}{2}\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

$$DC=\frac{\frac{1}{2}\sqrt{6}}{3}$$

Divide \frac{1}{2}\sqrt{6} by 3 to get \frac{1}{6}\sqrt{6}.

$$DC=\frac{1}{6}\sqrt{6}$$

The equation is in standard form.

$$DC=\frac{\sqrt{6}}{6}$$

Divide both sides by D.

$$\frac{DC}{D}=\frac{\sqrt{6}}{6D}$$

Dividing by D undoes the multiplication by D.

$$C=\frac{\sqrt{6}}{6D}$$

Solve for D

$$D=\frac{\sqrt{6}}{6C}$$

$$C\neq 0$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\frac{1}{2}\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$DC=\frac{\frac{1}{2}\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

$$DC=\frac{\frac{1}{2}\sqrt{6}}{3}$$

Divide \frac{1}{2}\sqrt{6} by 3 to get \frac{1}{6}\sqrt{6}.

$$DC=\frac{1}{6}\sqrt{6}$$

The equation is in standard form.

$$CD=\frac{\sqrt{6}}{6}$$

Divide both sides by C.

$$\frac{CD}{C}=\frac{\sqrt{6}}{6C}$$

Dividing by C undoes the multiplication by C.

$$D=\frac{\sqrt{6}}{6C}$$