Basic Math Examples

$\frac{1}{n + 9} \div \frac{6 - n}{3 n - 18}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{n + 9} \cdot \frac{3 n - 18}{6 - n}$

Step 2

Factor $3$ out of $3 n - 18$ .

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Step 2.1

Factor $3$ out of $3 n$ .

$\frac{1}{n + 9} \cdot \frac{3 (n) - 18}{6 - n}$

Step 2.2

Factor $3$ out of $- 18$ .

$\frac{1}{n + 9} \cdot \frac{3 n + 3 \cdot - 6}{6 - n}$

Step 2.3

Factor $3$ out of $3 n + 3 \cdot - 6$ .

$\frac{1}{n + 9} \cdot \frac{3 (n - 6)}{6 - n}$

Step 3

Cancel the common factor of $n - 6$ and $6 - n$ .

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Step 3.1

Factor $- 1$ out of $n$ .

$\frac{1}{n + 9} \cdot \frac{3 (- 1 (- n) - 6)}{6 - n}$

Step 3.2

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{1}{n + 9} \cdot \frac{3 (- 1 (- n) - 1 (6))}{6 - n}$

Step 3.3

Factor $- 1$ out of $- 1 (- n) - 1 (6)$ .

$\frac{1}{n + 9} \cdot \frac{3 (- 1 (- n + 6))}{6 - n}$

Step 3.4

Reorder terms.

$\frac{1}{n + 9} \cdot \frac{3 (- 1 (- n + 6))}{- n + 6}$

Step 3.5

Cancel the common factor.

$\frac{1}{n + 9} \cdot \frac{3 (- 1 (- n + 6))}{- n + 6}$

Step 3.6

Divide $3 \cdot (- 1)$ by $1$ .

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

Step 4

Multiply $3$ by $- 1$ .

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

Step 5

Combine $\frac{1}{n + 9}$ and $- 3$ .

$\frac{- 3}{n + 9}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{n + 9}$