Simplify ((a^2-81)/(49a+441))÷((a-9)/63)

$\frac{a^{2} - 81}{49 a + 441} \div \frac{a - 9}{63}$

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2} - 81}{49 a + 441} \cdot \frac{63}{a - 9}$

Simplify the numerator.

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Rewrite $81$ as $9^{2}$ .

$\frac{a^{2} - 9^{2}}{49 a + 441} \cdot \frac{63}{a - 9}$

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 $b = 9$ .

$\frac{(a + 9) (a - 9)}{49 a + 441} \cdot \frac{63}{a - 9}$

Simplify terms.

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Factor $49$ out of $49 a + 441$ .

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Factor $49$ out of $49 a$ .

$\frac{(a + 9) (a - 9)}{49 (a) + 441} \cdot \frac{63}{a - 9}$

Factor $49$ out of $441$ .

$\frac{(a + 9) (a - 9)}{49 a + 49 \cdot 9} \cdot \frac{63}{a - 9}$

Factor $49$ out of $49 a + 49 \cdot 9$ .

$\frac{(a + 9) (a - 9)}{49 (a + 9)} \cdot \frac{63}{a - 9}$

Cancel the common factor of $a - 9$ .

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Factor $a - 9$ out of $(a + 9) (a - 9)$ .

$\frac{(a - 9) (a + 9)}{49 (a + 9)} \cdot \frac{63}{a - 9}$

Cancel the common factor.

$\frac{(a - 9) (a + 9)}{49 (a + 9)} \cdot \frac{63}{a - 9}$

Rewrite the expression.

$\frac{a + 9}{49 (a + 9)} \cdot 63$

Cancel the common factor of $7$ .

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Factor $7$ out of $49 (a + 9)$ .

$\frac{a + 9}{7 (7 (a + 9))} \cdot 63$

Factor $7$ out of $63$ .

$\frac{a + 9}{7 (7 (a + 9))} \cdot (7 (9))$

Cancel the common factor.

$\frac{a + 9}{7 (7 (a + 9))} \cdot (7 \cdot 9)$

Rewrite the expression.

$\frac{a + 9}{7 (a + 9)} \cdot 9$

Combine $\frac{a + 9}{7 (a + 9)}$ and $9$ .

$\frac{(a + 9) \cdot 9}{7 (a + 9)}$

Cancel the common factor of $a + 9$ .

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Cancel the common factor.

$\frac{(a + 9) \cdot 9}{7 (a + 9)}$

Rewrite the expression.

$\frac{9}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{7}$

Decimal Form:

$1.\overline{285714}$

Mixed Number Form:

$1 \frac{2}{7}$

Simplify ((a^2-81)/(49a+441))÷((a-9)/63)

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