Solve frac{frac{sqrt{5}}{2}}{m-1/2}=1/DC

$$\frac { \frac { \sqrt { 5 } } { 2 } } { m - \frac { 1 } { 2 } } = \frac { 1 } { D C }$$

Solve for C

$$C=-\frac{\sqrt{5}\left(1-2m\right)}{5D}$$

$$m\neq \frac{1}{2}\text{ and }D\neq 0$$

Steps for Solving Linear Equation

Express \frac{\frac{\sqrt{5}}{2}}{m-\frac{1}{2}} as a single fraction.

$$\frac{\sqrt{5}}{2\left(m-\frac{1}{2}\right)}=\frac{1}{DC}$$

Use the distributive property to multiply 2 by m-\frac{1}{2}.

$$\frac{\sqrt{5}}{2m-1}=\frac{1}{DC}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{DC}=\frac{\sqrt{5}}{2m-1}$$

Variable C cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by CD\left(2m-1\right), the least common multiple of DC,2m-1.

$$2m-1=CD\sqrt{5}$$

Reorder the terms.

$$2m-1=\sqrt{5}CD$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{5}CD=2m-1$$

The equation is in standard form.

$$\sqrt{5}DC=2m-1$$

Divide both sides by \sqrt{5}D.

$$\frac{\sqrt{5}DC}{\sqrt{5}D}=\frac{2m-1}{\sqrt{5}D}$$

Dividing by \sqrt{5}D undoes the multiplication by \sqrt{5}D.

$$C=\frac{2m-1}{\sqrt{5}D}$$

Divide -1+2m by \sqrt{5}D.

$$C=\frac{\sqrt{5}\left(2m-1\right)}{5D}$$

Variable C cannot be equal to 0.

$$C=\frac{\sqrt{5}\left(2m-1\right)}{5D}\text{, }C\neq 0$$

Solve for D

$$D=-\frac{\sqrt{5}\left(1-2m\right)}{5C}$$

$$m\neq \frac{1}{2}\text{ and }C\neq 0$$

Steps for Solving Linear Equation

Express \frac{\frac{\sqrt{5}}{2}}{m-\frac{1}{2}} as a single fraction.

$$\frac{\sqrt{5}}{2\left(m-\frac{1}{2}\right)}=\frac{1}{DC}$$

Use the distributive property to multiply 2 by m-\frac{1}{2}.

$$\frac{\sqrt{5}}{2m-1}=\frac{1}{DC}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{DC}=\frac{\sqrt{5}}{2m-1}$$

Variable D cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by CD\left(2m-1\right), the least common multiple of DC,2m-1.

$$2m-1=CD\sqrt{5}$$

Reorder the terms.

$$2m-1=\sqrt{5}CD$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{5}CD=2m-1$$

Divide both sides by \sqrt{5}C.

$$\frac{\sqrt{5}CD}{\sqrt{5}C}=\frac{2m-1}{\sqrt{5}C}$$

Dividing by \sqrt{5}C undoes the multiplication by \sqrt{5}C.

$$D=\frac{2m-1}{\sqrt{5}C}$$

Divide -1+2m by \sqrt{5}C.

$$D=\frac{\sqrt{5}\left(2m-1\right)}{5C}$$

Variable D cannot be equal to 0.

$$D=\frac{\sqrt{5}\left(2m-1\right)}{5C}\text{, }D\neq 0$$