Basic Math Examples

$\frac{8 n}{8 n^{2} - 24} \div \frac{18 n^{2}}{4 n - 16}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 n}{8 n^{2} - 24} \cdot \frac{4 n - 16}{18 n^{2}}$

Step 2

Cancel the common factor of $2 n$ .

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Step 2.1

Factor $2 n$ out of $8 n$ .

$\frac{2 n (4)}{8 n^{2} - 24} \cdot \frac{4 n - 16}{18 n^{2}}$

Step 2.2

Factor $2 n$ out of $18 n^{2}$ .

$\frac{2 n (4)}{8 n^{2} - 24} \cdot \frac{4 n - 16}{2 n (9 n)}$

Step 2.3

Cancel the common factor.

$\frac{2 n \cdot 4}{8 n^{2} - 24} \cdot \frac{4 n - 16}{2 n (9 n)}$

Step 2.4

Rewrite the expression.

$\frac{4}{8 n^{2} - 24} \cdot \frac{4 n - 16}{9 n}$

Step 3

Multiply $\frac{4}{8 n^{2} - 24}$ by $\frac{4 n - 16}{9 n}$ .

$\frac{4 (4 n - 16)}{(8 n^{2} - 24) (9 n)}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $4$ out of $(8 n^{2} - 24) (9 n)$ .

$\frac{4 (4 n - 16)}{4 ((2 n^{2} - 6) (9 n))}$

Step 4.2

Cancel the common factor.

$\frac{4 (4 n - 16)}{4 ((2 n^{2} - 6) (9 n))}$

Step 4.3

Rewrite the expression.

$\frac{4 n - 16}{(2 n^{2} - 6) (9 n)}$

Step 5

Cancel the common factor of $4 n - 16$ and $2 n^{2} - 6$ .

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Step 5.1

Factor $2$ out of $4 n$ .

$\frac{2 (2 n) - 16}{(2 n^{2} - 6) (9 n)}$

Step 5.2

Factor $2$ out of $- 16$ .

$\frac{2 (2 n) + 2 \cdot - 8}{(2 n^{2} - 6) (9 n)}$

Step 5.3

Factor $2$ out of $2 (2 n) + 2 (- 8)$ .

$\frac{2 (2 n - 8)}{(2 n^{2} - 6) (9 n)}$

Step 5.4

Cancel the common factors.

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Step 5.4.1

Factor $2$ out of $(2 n^{2} - 6) (9 n)$ .

$\frac{2 (2 n - 8)}{2 ((n^{2} - 3) (9 n))}$

Step 5.4.2

Cancel the common factor.

$\frac{2 (2 n - 8)}{2 ((n^{2} - 3) (9 n))}$

Step 5.4.3

Rewrite the expression.

$\frac{2 n - 8}{(n^{2} - 3) (9 n)}$

Step 6

Factor $2$ out of $2 n - 8$ .

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Step 6.1

Factor $2$ out of $2 n$ .

$\frac{2 (n) - 8}{(n^{2} - 3) \cdot 9 n}$

Step 6.2

Factor $2$ out of $- 8$ .

$\frac{2 n + 2 \cdot - 4}{(n^{2} - 3) \cdot 9 n}$

Step 6.3

Factor $2$ out of $2 n + 2 \cdot - 4$ .

$\frac{2 (n - 4)}{(n^{2} - 3) \cdot 9 n}$

Step 7

Simplify the expression.

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Step 7.1

Move $9$ to the left of $n^{2} - 3$ .

$\frac{2 (n - 4)}{9 \cdot (n^{2} - 3) n}$

Step 7.2

Reorder factors in $\frac{2 (n - 4)}{9 (n^{2} - 3) n}$ .

$\frac{2 (n - 4)}{9 n (n^{2} - 3)}$