Simplify ((a-3)/7)÷((3-a)/21)

$\frac{a - 3}{7} \div \frac{3 - a}{21}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

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

Cancel the common factor.

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

Rewrite the expression.

$(a - 3) \frac{3}{3 - a}$

$(a - 3) \frac{3}{3 - a}$

Step 3

Multiply $a - 3$ by $\frac{3}{3 - a}$ .

$\frac{(a - 3) \cdot 3}{3 - a}$

Step 4

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

Factor $- 1$ out of $a$ .

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

Rewrite $- 3$ as $- 1 (3)$ .

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

Factor $- 1$ out of $- 1 (- a) - 1 (3)$ .

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

Reorder terms.

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

Cancel the common factor.

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

Divide $- 1 \cdot 3$ by $1$ .

$- 1 \cdot 3$

$- 1 \cdot 3$

Step 5

Multiply $- 1$ by $3$ .

$- 3$

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