Solve 1/2x+3/2x+1=operatorname{cog}45

$$\frac { 1 / 2 x + 3 } { 2 x + 1 } = \operatorname { cog } 45$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{x+6}{2g_{45}o\left(2x+1\right)}\text{, }&x\neq -\frac{1}{2}\text{ and }g_{45}\neq 0\text{ and }o\neq 0\\c\in \mathrm{C}\text{, }&\left(g_{45}=0\text{ or }o=0\right)\text{ and }x=-6\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+1.

$$\frac{1}{2}x+3=cog_{45}\left(2x+1\right)$$

Use the distributive property to multiply cog_{45} by 2x+1.

$$\frac{1}{2}x+3=2cog_{45}x+cog_{45}$$

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

$$2cog_{45}x+cog_{45}=\frac{1}{2}x+3$$

Combine all terms containing c.

$$\left(2og_{45}x+og_{45}\right)c=\frac{1}{2}x+3$$

The equation is in standard form.

$$\left(2g_{45}ox+g_{45}o\right)c=\frac{x}{2}+3$$

Divide both sides by 2og_{45}x+og_{45}.

$$\frac{\left(2g_{45}ox+g_{45}o\right)c}{2g_{45}ox+g_{45}o}=\frac{\frac{x}{2}+3}{2g_{45}ox+g_{45}o}$$

Dividing by 2og_{45}x+og_{45} undoes the multiplication by 2og_{45}x+og_{45}.

$$c=\frac{\frac{x}{2}+3}{2g_{45}ox+g_{45}o}$$

Divide \frac{x}{2}+3 by 2og_{45}x+og_{45}.

$$c=\frac{x+6}{2g_{45}o\left(2x+1\right)}$$

Solve for g_45 (complex solution)

$$\left\{\begin{matrix}g_{45}=\frac{x+6}{2co\left(2x+1\right)}\text{, }&x\neq -\frac{1}{2}\text{ and }o\neq 0\text{ and }c\neq 0\\g_{45}\in \mathrm{C}\text{, }&\left(o=0\text{ or }c=0\right)\text{ and }x=-6\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+1.

$$\frac{1}{2}x+3=cog_{45}\left(2x+1\right)$$

Use the distributive property to multiply cog_{45} by 2x+1.

$$\frac{1}{2}x+3=2cog_{45}x+cog_{45}$$

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

$$2cog_{45}x+cog_{45}=\frac{1}{2}x+3$$

Combine all terms containing g_{45}.

$$\left(2cox+co\right)g_{45}=\frac{1}{2}x+3$$

The equation is in standard form.

$$\left(2cox+co\right)g_{45}=\frac{x}{2}+3$$

Divide both sides by 2cox+co.

$$\frac{\left(2cox+co\right)g_{45}}{2cox+co}=\frac{\frac{x}{2}+3}{2cox+co}$$

Dividing by 2cox+co undoes the multiplication by 2cox+co.

$$g_{45}=\frac{\frac{x}{2}+3}{2cox+co}$$

Divide \frac{x}{2}+3 by 2cox+co.

$$g_{45}=\frac{x+6}{2co\left(2x+1\right)}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{x+6}{2g_{45}o\left(2x+1\right)}\text{, }&x\neq -\frac{1}{2}\text{ and }g_{45}\neq 0\text{ and }o\neq 0\\c\in \mathrm{R}\text{, }&\left(g_{45}=0\text{ or }o=0\right)\text{ and }x=-6\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+1.

$$\frac{1}{2}x+3=cog_{45}\left(2x+1\right)$$

Use the distributive property to multiply cog_{45} by 2x+1.

$$\frac{1}{2}x+3=2cog_{45}x+cog_{45}$$

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

$$2cog_{45}x+cog_{45}=\frac{1}{2}x+3$$

Combine all terms containing c.

$$\left(2og_{45}x+og_{45}\right)c=\frac{1}{2}x+3$$

The equation is in standard form.

$$\left(2g_{45}ox+g_{45}o\right)c=\frac{x}{2}+3$$

Divide both sides by 2og_{45}x+og_{45}.

$$\frac{\left(2g_{45}ox+g_{45}o\right)c}{2g_{45}ox+g_{45}o}=\frac{\frac{x}{2}+3}{2g_{45}ox+g_{45}o}$$

Dividing by 2og_{45}x+og_{45} undoes the multiplication by 2og_{45}x+og_{45}.

$$c=\frac{\frac{x}{2}+3}{2g_{45}ox+g_{45}o}$$

Divide \frac{x}{2}+3 by 2og_{45}x+og_{45}.

$$c=\frac{x+6}{2g_{45}o\left(2x+1\right)}$$

Solve for g_45

$$\left\{\begin{matrix}g_{45}=\frac{x+6}{2co\left(2x+1\right)}\text{, }&x\neq -\frac{1}{2}\text{ and }o\neq 0\text{ and }c\neq 0\\g_{45}\in \mathrm{R}\text{, }&\left(o=0\text{ or }c=0\right)\text{ and }x=-6\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+1.

$$\frac{1}{2}x+3=cog_{45}\left(2x+1\right)$$

Use the distributive property to multiply cog_{45} by 2x+1.

$$\frac{1}{2}x+3=2cog_{45}x+cog_{45}$$

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

$$2cog_{45}x+cog_{45}=\frac{1}{2}x+3$$

Combine all terms containing g_{45}.

$$\left(2cox+co\right)g_{45}=\frac{1}{2}x+3$$

The equation is in standard form.

$$\left(2cox+co\right)g_{45}=\frac{x}{2}+3$$

Divide both sides by 2cox+co.

$$\frac{\left(2cox+co\right)g_{45}}{2cox+co}=\frac{\frac{x}{2}+3}{2cox+co}$$

Dividing by 2cox+co undoes the multiplication by 2cox+co.

$$g_{45}=\frac{\frac{x}{2}+3}{2cox+co}$$

Divide \frac{x}{2}+3 by 2cox+co.

$$g_{45}=\frac{x+6}{2co\left(2x+1\right)}$$