Basic Math Examples

$\frac{3}{n^{2} - 9} \div \frac{3 n - 9}{n + 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{n^{2} - 9} \cdot \frac{n + 3}{3 n - 9}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{3}{n^{2} - 3^{2}} \cdot \frac{n + 3}{3 n - 9}$

Step 2.2

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 $b = 3$ .

$\frac{3}{(n + 3) (n - 3)} \cdot \frac{n + 3}{3 n - 9}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $n + 3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{3}{(n + 3) (n - 3)} \cdot \frac{n + 3}{3 n - 9}$

Step 3.1.2

Rewrite the expression.

$\frac{3}{n - 3} \cdot \frac{1}{3 n - 9}$

Step 3.2

Multiply $\frac{3}{n - 3}$ by $\frac{1}{3 n - 9}$ .

$\frac{3}{(n - 3) (3 n - 9)}$

Step 3.3

Cancel the common factor of $3$ and $3 n - 9$ .

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Step 3.3.1

Factor $3$ out of $3$ .

$\frac{3 \cdot 1}{(n - 3) (3 n - 9)}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $3$ out of $(n - 3) (3 n - 9)$ .

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

Step 3.3.2.2

Cancel the common factor.

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

Step 3.3.2.3

Rewrite the expression.

$\frac{1}{(n - 3) (n - 3)}$

Step 4

Simplify the denominator.

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Step 4.1

Raise $n - 3$ to the power of $1$ .

$\frac{1}{{(n - 3)}^{1} (n - 3)}$

Step 4.2

Raise $n - 3$ to the power of $1$ .

$\frac{1}{{(n - 3)}^{1} {(n - 3)}^{1}}$

Step 4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{{(n - 3)}^{1 + 1}}$

Step 4.4

Add $1$ and $1$ .

$\frac{1}{{(n - 3)}^{2}}$