Solve 3b-3/b-2=a

$$\frac{ 3b-3 }{ b-2 } =a$$

Solve for a

$$a=-\frac{3\left(b-1\right)}{2-b}$$

$$b\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by b-2.

$$3b-3=a\left(b-2\right)$$

Use the distributive property to multiply a by b-2.

$$3b-3=ab-2a$$

Swap sides so that all variable terms are on the left hand side.

$$ab-2a=3b-3$$

Combine all terms containing a.

$$\left(b-2\right)a=3b-3$$

Divide both sides by b-2.

$$\frac{\left(b-2\right)a}{b-2}=\frac{3b-3}{b-2}$$

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

$$a=\frac{3b-3}{b-2}$$

Divide -3+3b by b-2.

$$a=\frac{3\left(b-1\right)}{b-2}$$

Solve for b

$$b=-\frac{2a-3}{3-a}$$

$$a\neq 3$$

Steps for Solving Linear Equation

Variable b cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by b-2.

$$3b-3=a\left(b-2\right)$$

Use the distributive property to multiply a by b-2.

$$3b-3=ab-2a$$

Subtract ab from both sides.

$$3b-3-ab=-2a$$

Add 3 to both sides.

$$3b-ab=-2a+3$$

Combine all terms containing b.

$$\left(3-a\right)b=-2a+3$$

The equation is in standard form.

$$\left(3-a\right)b=3-2a$$

Divide both sides by 3-a.

$$\frac{\left(3-a\right)b}{3-a}=\frac{3-2a}{3-a}$$

Dividing by 3-a undoes the multiplication by 3-a.

$$b=\frac{3-2a}{3-a}$$

Variable b cannot be equal to 2.

$$b=\frac{3-2a}{3-a}\text{, }b\neq 2$$