Solve ax-ab-ax+bx=1-ab+b-x

$$a x - a b - a x + b x = 1 - a b + b - x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Combine ax and -ax to get 0.

$$-ab+bx=1-ab+b-x$$

Add ab to both sides.

$$-ab+bx+ab=1+b-x$$

Combine -ab and ab to get 0.

$$bx=1+b-x$$

Subtract b from both sides.

$$bx-b=1-x$$

Combine all terms containing b.

$$\left(x-1\right)b=1-x$$

Divide both sides by -1+x.

$$\frac{\left(x-1\right)b}{x-1}=\frac{1-x}{x-1}$$

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

$$b=\frac{1-x}{x-1}$$

Divide 1-x by -1+x.

$$b=-1$$

Solve for b

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

Steps for Solving Linear Equation

Combine ax and -ax to get 0.

$$-ab+bx=1-ab+b-x$$

Add ab to both sides.

$$-ab+bx+ab=1+b-x$$

Combine -ab and ab to get 0.

$$bx=1+b-x$$

Subtract b from both sides.

$$bx-b=1-x$$

Combine all terms containing b.

$$\left(x-1\right)b=1-x$$

Divide both sides by -1+x.

$$\frac{\left(x-1\right)b}{x-1}=\frac{1-x}{x-1}$$

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

$$b=\frac{1-x}{x-1}$$

Divide 1-x by -1+x.

$$b=-1$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

$$b=-1\text{ or }x=1$$

Solve for a

$$a\in \mathrm{R}$$

$$b=-1\text{ or }x=1$$