Basic Math Examples

$\frac{n - 9}{n} \div \frac{n^{2} - 81}{7 n^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{n - 9}{n} \cdot \frac{7 n^{2}}{n^{2} - 81}$

Step 2

Cancel the common factor of $n$ .

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Step 2.1

Factor $n$ out of $7 n^{2}$ .

$\frac{n - 9}{n} \cdot \frac{n (7 n)}{n^{2} - 81}$

Step 2.2

Cancel the common factor.

$\frac{n - 9}{n} \cdot \frac{n (7 n)}{n^{2} - 81}$

Step 2.3

Rewrite the expression.

$(n - 9) \frac{7 n}{n^{2} - 81}$

Step 3

Simplify the denominator.

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Step 3.1

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

$(n - 9) \frac{7 n}{n^{2} - 9^{2}}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = n$ and $b = 9$ .

$(n - 9) \frac{7 n}{(n + 9) (n - 9)}$

Step 4

Cancel the common factor of $n - 9$ .

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Step 4.1

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

$(n - 9) \frac{7 n}{(n - 9) (n + 9)}$

Step 4.2

Cancel the common factor.

$(n - 9) \frac{7 n}{(n - 9) (n + 9)}$

Step 4.3

Rewrite the expression.

$\frac{7 n}{n + 9}$