Simplify ((a^2-3ab)/(3b))÷(7a-21b)

$\frac{a^{2} - 3 a b}{3 b} \div (7 a - 21 b)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{a^{2} - 3 a b}{3 b}}{7 a - 21 b}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{a^{2} - 3 a b}{3 b} \cdot \frac{1}{7 a - 21 b}$

Step 3

Factor $a$ out of $a^{2} - 3 a b$ .

Factor $a$ out of $a^{2}$ .

$\frac{a \cdot a - 3 a b}{3 b} \cdot \frac{1}{7 a - 21 b}$

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

$\frac{a \cdot a + a (- 3 b)}{3 b} \cdot \frac{1}{7 a - 21 b}$

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

$\frac{a (a - 3 b)}{3 b} \cdot \frac{1}{7 a - 21 b}$

Step 4

Factor $7$ out of $7 a - 21 b$ .

Factor $7$ out of $7 a$ .

$\frac{a (a - 3 b)}{3 b} \cdot \frac{1}{7 (a) - 21 b}$

Factor $7$ out of $- 21 b$ .

$\frac{a (a - 3 b)}{3 b} \cdot \frac{1}{7 (a) + 7 (- 3 b)}$

Factor $7$ out of $7 (a) + 7 (- 3 b)$ .

$\frac{a (a - 3 b)}{3 b} \cdot \frac{1}{7 (a - 3 b)}$

Step 5

Cancel the common factor of $a - 3 b$ .

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

$\frac{(a - 3 b) a}{3 b} \cdot \frac{1}{7 (a - 3 b)}$

Factor $a - 3 b$ out of $7 (a - 3 b)$ .

$\frac{(a - 3 b) a}{3 b} \cdot \frac{1}{(a - 3 b) \cdot 7}$

Cancel the common factor.

$\frac{(a - 3 b) a}{3 b} \cdot \frac{1}{(a - 3 b) \cdot 7}$

Rewrite the expression.

$\frac{a}{3 b} \cdot \frac{1}{7}$

Step 6

Multiply $\frac{a}{3 b}$ by $\frac{1}{7}$ .

$\frac{a}{3 b \cdot 7}$

Step 7

Multiply $7$ by $3$ .

$\frac{a}{21 b}$