Pre-Algebra Examples

$\frac{n^{2} + 7 n + 12}{16 n^{2}} \div \frac{n + 3}{2 n}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{n^{2} + 7 n + 12}{16 n^{2}} \cdot \frac{2 n}{n + 3}$

Step 2

Cancel the common factor of $2 n$ .

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Step 2.1

Factor $2 n$ out of $16 n^{2}$ .

$\frac{n^{2} + 7 n + 12}{2 n (8 n)} \cdot \frac{2 n}{n + 3}$

Step 2.2

Cancel the common factor.

$\frac{n^{2} + 7 n + 12}{2 n (8 n)} \cdot \frac{2 n}{n + 3}$

Step 2.3

Rewrite the expression.

$\frac{n^{2} + 7 n + 12}{8 n} \cdot \frac{1}{n + 3}$

Step 3

Multiply $\frac{n^{2} + 7 n + 12}{8 n}$ by $\frac{1}{n + 3}$ .

$\frac{n^{2} + 7 n + 12}{8 n (n + 3)}$

Step 4

Factor $n^{2} + 7 n + 12$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $12$ and whose sum is $7$ .

$3, 4$

Step 4.2

Write the factored form using these integers.

$\frac{(n + 3) (n + 4)}{8 n (n + 3)}$

Step 5

Cancel the common factor of $n + 3$ .

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Step 5.1

Cancel the common factor.

$\frac{(n + 3) (n + 4)}{8 n (n + 3)}$

Step 5.2

Rewrite the expression.

$\frac{n + 4}{8 n}$

Step 6

Split the fraction $\frac{n + 4}{8 n}$ into two fractions.

$\frac{n}{8 n} + \frac{4}{8 n}$

Step 7

Cancel the common factor of $n$ .

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Step 7.1

Cancel the common factor.

$\frac{n}{8 n} + \frac{4}{8 n}$

Step 7.2

Rewrite the expression.

$\frac{1}{8} + \frac{4}{8 n}$

Step 8

Cancel the common factor of $4$ and $8$ .

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Step 8.1

Factor $4$ out of $4$ .

$\frac{1}{8} + \frac{4 (1)}{8 n}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $4$ out of $8 n$ .

$\frac{1}{8} + \frac{4 (1)}{4 (2 n)}$

Step 8.2.2

Cancel the common factor.

$\frac{1}{8} + \frac{4 \cdot 1}{4 (2 n)}$

Step 8.2.3

Rewrite the expression.

$\frac{1}{8} + \frac{1}{2 n}$