Solve (x-1)*P(x)=x^2-3x+2

$$( x - 1 ) \cdot P ( x ) = x ^ { 2 } - 3 x + 2$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=\frac{x-2}{x}\text{, }&x\neq 0\\P\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by P.

$$\left(xP-P\right)x=x^{2}-3x+2$$

Use the distributive property to multiply xP-P by x.

$$Px^{2}-Px=x^{2}-3x+2$$

Combine all terms containing P.

$$\left(x^{2}-x\right)P=x^{2}-3x+2$$

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

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

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

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

Divide \left(-2+x\right)\left(-1+x\right) by x^{2}-x.

$$P=\frac{x-2}{x}$$

Solve for P

$$\left\{\begin{matrix}P=\frac{x-2}{x}\text{, }&x\neq 0\\P\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by P.

$$\left(xP-P\right)x=x^{2}-3x+2$$

Use the distributive property to multiply xP-P by x.

$$Px^{2}-Px=x^{2}-3x+2$$

Combine all terms containing P.

$$\left(x^{2}-x\right)P=x^{2}-3x+2$$

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

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

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

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

Divide \left(-2+x\right)\left(-1+x\right) by x^{2}-x.

$$P=\frac{x-2}{x}$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=-\frac{2}{P-1}\text{, }&P\neq 1\end{matrix}\right.$$