Basic Math Examples

$\frac{18 x + 18}{16 x + 32} \cdot \frac{4 x + 8}{6 x^{2} - 6}$

Step 1

Simplify with factoring out.

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Step 1.1

Factor $18$ out of $18 x + 18$ .

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Step 1.1.1

Factor $18$ out of $18 x$ .

$\frac{18 (x) + 18}{16 x + 32} \cdot \frac{4 x + 8}{6 x^{2} - 6}$

Step 1.1.2

Factor $18$ out of $18$ .

$\frac{18 (x) + 18 (1)}{16 x + 32} \cdot \frac{4 x + 8}{6 x^{2} - 6}$

Step 1.1.3

Factor $18$ out of $18 (x) + 18 (1)$ .

$\frac{18 (x + 1)}{16 x + 32} \cdot \frac{4 x + 8}{6 x^{2} - 6}$

Step 1.2

Factor $16$ out of $16 x + 32$ .

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Step 1.2.1

Factor $16$ out of $16 x$ .

$\frac{18 (x + 1)}{16 (x) + 32} \cdot \frac{4 x + 8}{6 x^{2} - 6}$

Step 1.2.2

Factor $16$ out of $32$ .

$\frac{18 (x + 1)}{16 x + 16 \cdot 2} \cdot \frac{4 x + 8}{6 x^{2} - 6}$

Step 1.2.3

Factor $16$ out of $16 x + 16 \cdot 2$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 x + 8}{6 x^{2} - 6}$

Step 1.3

Factor $4$ out of $4 x + 8$ .

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Step 1.3.1

Factor $4$ out of $4 x$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 (x) + 8}{6 x^{2} - 6}$

Step 1.3.2

Factor $4$ out of $8$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 x + 4 \cdot 2}{6 x^{2} - 6}$

Step 1.3.3

Factor $4$ out of $4 x + 4 \cdot 2$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 x^{2} - 6}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $6$ out of $6 x^{2} - 6$ .

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Step 2.1.1

Factor $6$ out of $6 x^{2}$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 (x^{2}) - 6}$

Step 2.1.2

Factor $6$ out of $- 6$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 (x^{2}) + 6 (- 1)}$

Step 2.1.3

Factor $6$ out of $6 (x^{2}) + 6 (- 1)$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 (x^{2} - 1)}$

Step 2.2

Rewrite $1$ as $1^{2}$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 (x^{2} - 1^{2})}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{18 (x + 1)}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 (x + 1) (x - 1)}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $6 (x + 1)$ .

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Step 3.1.1

Factor $6 (x + 1)$ out of $18 (x + 1)$ .

$\frac{6 (x + 1) (3)}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 (x + 1) (x - 1)}$

Step 3.1.2

Cancel the common factor.

$\frac{6 (x + 1) \cdot 3}{16 (x + 2)} \cdot \frac{4 (x + 2)}{6 (x + 1) (x - 1)}$

Step 3.1.3

Rewrite the expression.

$\frac{3}{16 (x + 2)} \cdot \frac{4 (x + 2)}{x - 1}$

Step 3.2

Cancel the common factor of $4 (x + 2)$ .

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Step 3.2.1

Factor $4 (x + 2)$ out of $16 (x + 2)$ .

$\frac{3}{4 (x + 2) (4)} \cdot \frac{4 (x + 2)}{x - 1}$

Step 3.2.2

Cancel the common factor.

$\frac{3}{4 (x + 2) \cdot 4} \cdot \frac{4 (x + 2)}{x - 1}$

Step 3.2.3

Rewrite the expression.

$\frac{3}{4} \cdot \frac{1}{x - 1}$

Step 3.3

Multiply $\frac{3}{4}$ by $\frac{1}{x - 1}$ .

$\frac{3}{4 (x - 1)}$