Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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 $b = 9$ .

$\frac{2 n}{(n + 9) (n - 9)} \cdot \frac{n - 9}{n}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $n$ .

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Step 2.1.1

Factor $n$ out of $2 n$ .

$\frac{n \cdot 2}{(n + 9) (n - 9)} \cdot \frac{n - 9}{n}$

Step 2.1.2

Cancel the common factor.

$\frac{n \cdot 2}{(n + 9) (n - 9)} \cdot \frac{n - 9}{n}$

Step 2.1.3

Rewrite the expression.

$\frac{2}{(n + 9) (n - 9)} \cdot (n - 9)$

Step 2.2

Cancel the common factor of $n - 9$ .

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Step 2.2.1

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

$\frac{2}{(n - 9) (n + 9)} \cdot (n - 9)$

Step 2.2.2

Cancel the common factor.

$\frac{2}{(n - 9) (n + 9)} \cdot (n - 9)$

Step 2.2.3

Rewrite the expression.

$\frac{2}{n + 9}$