Solve (m-1)x^2-2(m+1)x+9=0

$$( m - 1 ) x ^ { 2 } - 2 ( m + 1 ) x + 9 = 0$$

Solve for m

$$m=-\frac{9-2x-x^{2}}{x\left(x-2\right)}$$

$$x\neq 2\text{ and }x\neq 0$$

Steps for Solving Linear Equation

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

$$mx^{2}-x^{2}-2\left(m+1\right)x+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$mx^{2}-x^{2}-2\left(m+1\right)x=-9$$

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

$$mx^{2}-x^{2}+\left(-2m-2\right)x=-9$$

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

$$mx^{2}-x^{2}-2mx-2x=-9$$

Add x^{2} to both sides.

$$mx^{2}-2mx-2x=-9+x^{2}$$

Add 2x to both sides.

$$mx^{2}-2mx=-9+x^{2}+2x$$

Combine all terms containing m.

$$\left(x^{2}-2x\right)m=-9+x^{2}+2x$$

The equation is in standard form.

$$\left(x^{2}-2x\right)m=x^{2}+2x-9$$

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

$$\frac{\left(x^{2}-2x\right)m}{x^{2}-2x}=\frac{x^{2}+2x-9}{x^{2}-2x}$$

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

$$m=\frac{x^{2}+2x-9}{x^{2}-2x}$$

Divide -9+x^{2}+2x by x^{2}-2x.

$$m=\frac{x^{2}+2x-9}{x\left(x-2\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{\left(m-5\right)\left(m-2\right)}+m+1}{m-1}\text{; }x=\frac{-\sqrt{\left(m-5\right)\left(m-2\right)}+m+1}{m-1}\text{, }&m\neq 1\\x=\frac{9}{4}\text{, }&m=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{\left(m-5\right)\left(m-2\right)}+m+1}{m-1}\text{; }x=\frac{-\sqrt{\left(m-5\right)\left(m-2\right)}+m+1}{m-1}\text{, }&m\geq 5\text{ or }\left(m\neq 1\text{ and }m\leq 2\right)\\x=\frac{9}{4}\text{, }&m=1\end{matrix}\right.$$