Solve mx-x=m^2-1

$$m x - x = m ^ { 2 } - 1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=m+1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(m-1\right)x=m^{2}-1$$

Divide both sides by -1+m.

$$\frac{\left(m-1\right)x}{m-1}=\frac{m^{2}-1}{m-1}$$

Dividing by -1+m undoes the multiplication by -1+m.

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

Divide m^{2}-1 by -1+m.

$$x=m+1$$

Solve for x

$$\left\{\begin{matrix}\\x=m+1\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&m=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(m-1\right)x=m^{2}-1$$

Divide both sides by m-1.

$$\frac{\left(m-1\right)x}{m-1}=\frac{m^{2}-1}{m-1}$$

Dividing by m-1 undoes the multiplication by m-1.

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

Divide m^{2}-1 by m-1.

$$x=m+1$$

Solve for m

$$m=1$$

$$m=x-1$$