Simplify b/6-(3a-2b)/6

$\frac{b}{6} - \frac{3 a - 2 b}{6}$

Combine the numerators over the common denominator.

$\frac{b - (3 a - 2 b)}{6}$

Simplify each term.

Apply the distributive property.

$\frac{b - (3 a) - (- 2 b)}{6}$

Multiply $3$ by $- 1$ .

$\frac{b - 3 a - (- 2 b)}{6}$

Multiply $- 2$ by $- 1$ .

$\frac{b - 3 a + 2 b}{6}$

Simplify terms.

Add $b$ and $2 b$ .

$\frac{- 3 a + 3 b}{6}$

Cancel the common factor of $- 3 a + 3 b$ and $6$ .

Factor $3$ out of $- 3 a$ .

$\frac{3 (- a) + 3 b}{6}$

Factor $3$ out of $3 b$ .

$\frac{3 (- a) + 3 (b)}{6}$

Factor $3$ out of $3 (- a) + 3 (b)$ .

$\frac{3 (- a + b)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 (- a + b)}{3 (2)}$

Cancel the common factor.

$\frac{3 (- a + b)}{3 \cdot 2}$

Rewrite the expression.

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

Factor $- 1$ out of $- a$ .

$\frac{- (a) + b}{2}$

Factor $- 1$ out of $b$ .

$\frac{- (a) - 1 (- b)}{2}$

Factor $- 1$ out of $- (a) - 1 (- b)$ .

$\frac{- (a - b)}{2}$

Simplify the expression.

Rewrite $- (a - b)$ as $- 1 (a - b)$ .

$\frac{- 1 (a - b)}{2}$

Move the negative in front of the fraction.

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