Simplify ((4a-28)/6)÷((a^2-49)/(3a-21))

$\frac{4 a - 28}{6} \div \frac{a^{2} - 49}{3 a - 21}$

To divide by a fraction, multiply by its reciprocal.

$\frac{4 a - 28}{6} \cdot \frac{3 a - 21}{a^{2} - 49}$

Simplify terms.

Cancel the common factor of $4 a - 28$ and $6$ .

Factor $2$ out of $4 a$ .

$\frac{2 (2 a) - 28}{6} \cdot \frac{3 a - 21}{a^{2} - 49}$

Factor $2$ out of $- 28$ .

$\frac{2 (2 a) + 2 (- 14)}{6} \cdot \frac{3 a - 21}{a^{2} - 49}$

Factor $2$ out of $2 (2 a) + 2 (- 14)$ .

$\frac{2 (2 a - 14)}{6} \cdot \frac{3 a - 21}{a^{2} - 49}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 (2 a - 14)}{2 (3)} \cdot \frac{3 a - 21}{a^{2} - 49}$

Cancel the common factor.

$\frac{2 (2 a - 14)}{2 \cdot 3} \cdot \frac{3 a - 21}{a^{2} - 49}$

Rewrite the expression.

$\frac{2 a - 14}{3} \cdot \frac{3 a - 21}{a^{2} - 49}$

Factor $2$ out of $2 a - 14$ .

Factor $2$ out of $2 a$ .

$\frac{2 (a) - 14}{3} \cdot \frac{3 a - 21}{a^{2} - 49}$

Factor $2$ out of $- 14$ .

$\frac{2 a + 2 \cdot - 7}{3} \cdot \frac{3 a - 21}{a^{2} - 49}$

Factor $2$ out of $2 a + 2 \cdot - 7$ .

$\frac{2 (a - 7)}{3} \cdot \frac{3 a - 21}{a^{2} - 49}$

Factor $3$ out of $3 a - 21$ .

Factor $3$ out of $3 a$ .

$\frac{2 (a - 7)}{3} \cdot \frac{3 (a) - 21}{a^{2} - 49}$

Factor $3$ out of $- 21$ .

$\frac{2 (a - 7)}{3} \cdot \frac{3 a + 3 \cdot - 7}{a^{2} - 49}$

Factor $3$ out of $3 a + 3 \cdot - 7$ .

$\frac{2 (a - 7)}{3} \cdot \frac{3 (a - 7)}{a^{2} - 49}$

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$\frac{2 (a - 7)}{3} \cdot \frac{3 (a - 7)}{a^{2} - 7^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = 7$ .

$\frac{2 (a - 7)}{3} \cdot \frac{3 (a - 7)}{(a + 7) (a - 7)}$

Simplify terms.

Cancel the common factor of $a - 7$ .

Factor $a - 7$ out of $2 (a - 7)$ .

$\frac{(a - 7) \cdot 2}{3} \cdot \frac{3 (a - 7)}{(a + 7) (a - 7)}$

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

$\frac{(a - 7) \cdot 2}{3} \cdot \frac{3 (a - 7)}{(a - 7) (a + 7)}$

Cancel the common factor.

$\frac{(a - 7) \cdot 2}{3} \cdot \frac{3 (a - 7)}{(a - 7) (a + 7)}$

Rewrite the expression.

$\frac{2}{3} \cdot \frac{3 (a - 7)}{a + 7}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 (a - 7)}{a + 7}$

Rewrite the expression.

$2 \frac{a - 7}{a + 7}$

Combine $2$ and $\frac{a - 7}{a + 7}$ .

$\frac{2 (a - 7)}{a + 7}$

Simplify ((4a-28)/6)÷((a^2-49)/(3a-21))

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