Algebra Examples

$\frac{x + 8}{18} \div \frac{2 x^{2} + 16 x}{16 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 8}{18} \cdot \frac{16 x}{2 x^{2} + 16 x}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $18$ .

$\frac{x + 8}{2 (9)} \cdot \frac{16 x}{2 x^{2} + 16 x}$

Step 2.2

Factor $2$ out of $16 x$ .

$\frac{x + 8}{2 (9)} \cdot \frac{2 (8 x)}{2 x^{2} + 16 x}$

Step 2.3

Cancel the common factor.

$\frac{x + 8}{2 \cdot 9} \cdot \frac{2 (8 x)}{2 x^{2} + 16 x}$

Step 2.4

Rewrite the expression.

$\frac{x + 8}{9} \cdot \frac{8 x}{2 x^{2} + 16 x}$

Step 3

Multiply $\frac{x + 8}{9}$ by $\frac{8 x}{2 x^{2} + 16 x}$ .

$\frac{(x + 8) (8 x)}{9 (2 x^{2} + 16 x)}$

Step 4

Simplify the denominator.

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Step 4.1

Factor $2 x$ out of $2 x^{2} + 16 x$ .

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Step 4.1.1

Factor $2 x$ out of $2 x^{2}$ .

$\frac{(x + 8) \cdot 8 x}{9 (2 x (x) + 16 x)}$

Step 4.1.2

Factor $2 x$ out of $16 x$ .

$\frac{(x + 8) \cdot 8 x}{9 (2 x (x) + 2 x (8))}$

Step 4.1.3

Factor $2 x$ out of $2 x (x) + 2 x (8)$ .

$\frac{(x + 8) \cdot 8 x}{9 (2 x (x + 8))}$

$\frac{(x + 8) \cdot 8 x}{9 \cdot 2 x (x + 8)}$

Step 4.2

Multiply $9$ by $2$ .

$\frac{(x + 8) \cdot 8 x}{18 x (x + 8)}$

Step 5

Cancel the common factor of $x + 8$ .

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Step 5.1

Cancel the common factor.

$\frac{(x + 8) \cdot 8 x}{18 x (x + 8)}$

Step 5.2

Rewrite the expression.

$\frac{8 x}{18 x}$

Step 6

Cancel the common factor of $8$ and $18$ .

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Step 6.1

Factor $2$ out of $8 x$ .

$\frac{2 (4 x)}{18 x}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $18 x$ .

$\frac{2 (4 x)}{2 (9 x)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (4 x)}{2 (9 x)}$

Step 6.2.3

Rewrite the expression.

$\frac{4 x}{9 x}$

Step 7

Cancel the common factor of $x$ .

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Step 7.1

Cancel the common factor.

$\frac{4 x}{9 x}$

Step 7.2

Rewrite the expression.

$\frac{4}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$