Finite Math Examples

$\frac{3 x^{2} - 3}{6 x - 150} \cdot \frac{12 x + 60}{2 x - 2}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $3$ out of $3 x^{2} - 3$ .

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Step 1.1.1

Factor $3$ out of $3 x^{2}$ .

$\frac{3 (x^{2}) - 3}{6 x - 150} \cdot \frac{12 x + 60}{2 x - 2}$

Step 1.1.2

Factor $3$ out of $- 3$ .

$\frac{3 (x^{2}) + 3 (- 1)}{6 x - 150} \cdot \frac{12 x + 60}{2 x - 2}$

Step 1.1.3

Factor $3$ out of $3 (x^{2}) + 3 (- 1)$ .

$\frac{3 (x^{2} - 1)}{6 x - 150} \cdot \frac{12 x + 60}{2 x - 2}$

Step 1.2

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

$\frac{3 (x^{2} - 1^{2})}{6 x - 150} \cdot \frac{12 x + 60}{2 x - 2}$

Step 1.3

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 $b = 1$ .

$\frac{3 (x + 1) (x - 1)}{6 x - 150} \cdot \frac{12 x + 60}{2 x - 2}$

Step 2

Simplify terms.

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Step 2.1

Factor $6$ out of $6 x - 150$ .

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Step 2.1.1

Factor $6$ out of $6 x$ .

$\frac{3 (x + 1) (x - 1)}{6 (x) - 150} \cdot \frac{12 x + 60}{2 x - 2}$

Step 2.1.2

Factor $6$ out of $- 150$ .

$\frac{3 (x + 1) (x - 1)}{6 x + 6 \cdot - 25} \cdot \frac{12 x + 60}{2 x - 2}$

Step 2.1.3

Factor $6$ out of $6 x + 6 \cdot - 25$ .

$\frac{3 (x + 1) (x - 1)}{6 (x - 25)} \cdot \frac{12 x + 60}{2 x - 2}$

Step 2.2

Factor $12$ out of $12 x + 60$ .

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Step 2.2.1

Factor $12$ out of $12 x$ .

$\frac{3 (x + 1) (x - 1)}{6 (x - 25)} \cdot \frac{12 (x) + 60}{2 x - 2}$

Step 2.2.2

Factor $12$ out of $60$ .

$\frac{3 (x + 1) (x - 1)}{6 (x - 25)} \cdot \frac{12 x + 12 \cdot 5}{2 x - 2}$

Step 2.2.3

Factor $12$ out of $12 x + 12 \cdot 5$ .

$\frac{3 (x + 1) (x - 1)}{6 (x - 25)} \cdot \frac{12 (x + 5)}{2 x - 2}$

Step 2.3

Factor $2$ out of $2 x - 2$ .

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Step 2.3.1

Factor $2$ out of $2 x$ .

$\frac{3 (x + 1) (x - 1)}{6 (x - 25)} \cdot \frac{12 (x + 5)}{2 (x) - 2}$

Step 2.3.2

Factor $2$ out of $- 2$ .

$\frac{3 (x + 1) (x - 1)}{6 (x - 25)} \cdot \frac{12 (x + 5)}{2 (x) + 2 (- 1)}$

Step 2.3.3

Factor $2$ out of $2 (x) + 2 (- 1)$ .

$\frac{3 (x + 1) (x - 1)}{6 (x - 25)} \cdot \frac{12 (x + 5)}{2 (x - 1)}$

Step 2.4

Cancel the common factor of $x - 1$ .

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Step 2.4.1

Factor $x - 1$ out of $3 (x + 1) (x - 1)$ .

$\frac{(x - 1) (3 (x + 1))}{6 (x - 25)} \cdot \frac{12 (x + 5)}{2 (x - 1)}$

Step 2.4.2

Factor $x - 1$ out of $2 (x - 1)$ .

$\frac{(x - 1) (3 (x + 1))}{6 (x - 25)} \cdot \frac{12 (x + 5)}{(x - 1) \cdot 2}$

Step 2.4.3

Cancel the common factor.

$\frac{(x - 1) (3 (x + 1))}{6 (x - 25)} \cdot \frac{12 (x + 5)}{(x - 1) \cdot 2}$

Step 2.4.4

Rewrite the expression.

$\frac{3 (x + 1)}{6 (x - 25)} \cdot \frac{12 (x + 5)}{2}$

Step 2.5

Cancel the common factor of $6$ .

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Step 2.5.1

Factor $6$ out of $12 (x + 5)$ .

$\frac{3 (x + 1)}{6 (x - 25)} \cdot \frac{6 (2 (x + 5))}{2}$

Step 2.5.2

Cancel the common factor.

$\frac{3 (x + 1)}{6 (x - 25)} \cdot \frac{6 (2 (x + 5))}{2}$

Step 2.5.3

Rewrite the expression.

$\frac{3 (x + 1)}{x - 25} \cdot \frac{2 (x + 5)}{2}$

Step 2.6

Multiply $\frac{3 (x + 1)}{x - 25}$ by $\frac{2 (x + 5)}{2}$ .

$\frac{3 (x + 1) (2 (x + 5))}{(x - 25) \cdot 2}$

Step 2.7

Multiply $2$ by $3$ .

$\frac{6 (x + 1) (x + 5)}{(x - 25) \cdot 2}$

Step 2.8

Cancel the common factor of $6$ and $2$ .

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Step 2.8.1

Factor $2$ out of $6 (x + 1) (x + 5)$ .

$\frac{2 (3 (x + 1) (x + 5))}{(x - 25) \cdot 2}$

Step 2.8.2

Cancel the common factors.

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Step 2.8.2.1

Factor $2$ out of $(x - 25) \cdot 2$ .

$\frac{2 (3 (x + 1) (x + 5))}{2 \cdot (x - 25)}$

Step 2.8.2.2

Cancel the common factor.

$\frac{2 (3 (x + 1) (x + 5))}{2 \cdot (x - 25)}$

Step 2.8.2.3

Rewrite the expression.

$\frac{3 (x + 1) (x + 5)}{x - 25}$