Solve ab-a=-b+1quad[a]

$$a b - a = - b + 1 \quad [ a ]$$

Solve for a

$$a=-\frac{b}{b-2}$$

$$b\neq 2$$

Steps for Solving Linear Equation

Subtract 1a from both sides.

$$ab-a-a=-b$$

Combine -a and -a to get -2a.

$$ab-2a=-b$$

Combine all terms containing a.

$$\left(b-2\right)a=-b$$

Divide both sides by b-2.

$$\frac{\left(b-2\right)a}{b-2}=-\frac{b}{b-2}$$

Dividing by b-2 undoes the multiplication by b-2.

$$a=-\frac{b}{b-2}$$

Solve for b

$$b=\frac{2a}{a+1}$$

$$a\neq -1$$

Steps for Solving Linear Equation

Add b to both sides.

$$ab-a+b=1a$$

Add a to both sides.

$$ab+b=1a+a$$

Combine 1a and a to get 2a.

$$ab+b=2a$$

Combine all terms containing b.

$$\left(a+1\right)b=2a$$

Divide both sides by a+1.

$$\frac{\left(a+1\right)b}{a+1}=\frac{2a}{a+1}$$

Dividing by a+1 undoes the multiplication by a+1.

$$b=\frac{2a}{a+1}$$