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

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

Solve for m

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

$$x\neq 1$$

Steps for Solving Linear Equation

Add 1 to both sides. Anything plus zero gives itself.

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

Use the distributive property to multiply -2 by m+1.

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

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

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

Add 2x to both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

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

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

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

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{m+\sqrt{3m+1}+1}{m}\text{; }x=\frac{m-\sqrt{3m+1}+1}{m}\text{, }&m\neq 0\\x=-\frac{1}{2}\text{, }&m=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{m+\sqrt{3m+1}+1}{m}\text{; }x=\frac{m-\sqrt{3m+1}+1}{m}\text{, }&m\neq 0\text{ and }m\geq -\frac{1}{3}\\x=-\frac{1}{2}\text{, }&m=0\end{matrix}\right.$$