Solve for a 3ab-1=2ab-3

$3 a b - 1 = 2 a b - 3$

Move all terms containing $a$ to the left side of the equation.

Subtract $2 a b$ from both sides of the equation.

$3 a b - 1 - 2 a b = - 3$

Subtract $2 a b$ from $3 a b$ .

$1 a b - 1 = - 3$

Multiply $a$ by $1$ .

$a b - 1 = - 3$

Move all terms not containing $a$ to the right side of the equation.

Add $1$ to both sides of the equation.

$a b = - 3 + 1$

Add $- 3$ and $1$ .

$a b = - 2$

Divide each term in $a b = - 2$ by $b$ and simplify.

Divide each term in $a b = - 2$ by $b$ .

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

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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