Solve (m-1)x^2-2mx+m=0

$$( m - 1 ) x ^ { 2 } - 2 m x + m = 0$$

Solve for m

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

$$x\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-1 by x^{2}.

$$mx^{2}-x^{2}-2mx+m=0$$

Add x^{2} to both sides. Anything plus zero gives itself.

$$mx^{2}-2mx+m=x^{2}$$

Combine all terms containing m.

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

Divide both sides by x^{2}-2x+1.

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

Dividing by x^{2}-2x+1 undoes the multiplication by x^{2}-2x+1.

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{m}\left(\sqrt{m}+1\right)}{m-1}\text{; }x=\frac{\sqrt{m}\left(\sqrt{m}-1\right)}{m-1}\text{, }&m\neq 1\\x=\frac{1}{2}\text{, }&m=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{m}\left(\sqrt{m}+1\right)}{m-1}\text{; }x=\frac{\sqrt{m}\left(\sqrt{m}-1\right)}{m-1}\text{, }&m\neq 1\text{ and }m\geq 0\\x=\frac{1}{2}\text{, }&m=1\end{matrix}\right.$$