Solve mx/4-x-2/m=1

$$\frac { m x } { 4 } - \frac { x - 2 } { m } = 1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{4}{m+2}\text{, }&m\neq -2\text{ and }m\neq 0\\x\in \mathrm{C}\text{, }&m=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4m, the least common multiple of 4,m.

$$mmx-4\left(x-2\right)=4m$$

Multiply m and m to get m^{2}.

$$m^{2}x-4\left(x-2\right)=4m$$

Use the distributive property to multiply -4 by x-2.

$$m^{2}x-4x+8=4m$$

Subtract 8 from both sides.

$$m^{2}x-4x=4m-8$$

Combine all terms containing x.

$$\left(m^{2}-4\right)x=4m-8$$

Divide both sides by m^{2}-4.

$$\frac{\left(m^{2}-4\right)x}{m^{2}-4}=\frac{4m-8}{m^{2}-4}$$

Dividing by m^{2}-4 undoes the multiplication by m^{2}-4.

$$x=\frac{4m-8}{m^{2}-4}$$

Divide -8+4m by m^{2}-4.

$$x=\frac{4}{m+2}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{4}{m+2}\text{, }&m\neq -2\text{ and }m\neq 0\\x\in \mathrm{R}\text{, }&m=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4m, the least common multiple of 4,m.

$$mmx-4\left(x-2\right)=4m$$

Multiply m and m to get m^{2}.

$$m^{2}x-4\left(x-2\right)=4m$$

Use the distributive property to multiply -4 by x-2.

$$m^{2}x-4x+8=4m$$

Subtract 8 from both sides.

$$m^{2}x-4x=4m-8$$

Combine all terms containing x.

$$\left(m^{2}-4\right)x=4m-8$$

Divide both sides by m^{2}-4.

$$\frac{\left(m^{2}-4\right)x}{m^{2}-4}=\frac{4m-8}{m^{2}-4}$$

Dividing by m^{2}-4 undoes the multiplication by m^{2}-4.

$$x=\frac{4m-8}{m^{2}-4}$$

Divide -8+4m by m^{2}-4.

$$x=\frac{4}{m+2}$$

Solve for m

$$\left\{\begin{matrix}\\m=2\text{, }&\text{unconditionally}\\m=-2+\frac{4}{x}\text{, }&x\neq 2\text{ and }x\neq 0\end{matrix}\right.$$