Basic Math Examples

$\frac{6 c^{2} - 4 c - 30}{3 c^{2} - 12}$

Step 1

Factor $2$ out of $6 c^{2} - 4 c - 30$ .

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Step 1.1

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

$\frac{2 (3 c^{2}) - 4 c - 30}{3 c^{2} - 12}$

Step 1.2

Factor $2$ out of $- 4 c$ .

$\frac{2 (3 c^{2}) + 2 (- 2 c) - 30}{3 c^{2} - 12}$

Step 1.3

Factor $2$ out of $- 30$ .

$\frac{2 (3 c^{2}) + 2 (- 2 c) + 2 (- 15)}{3 c^{2} - 12}$

Step 1.4

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

$\frac{2 (3 c^{2} - 2 c) + 2 (- 15)}{3 c^{2} - 12}$

Step 1.5

Factor $2$ out of $2 (3 c^{2} - 2 c) + 2 (- 15)$ .

$\frac{2 (3 c^{2} - 2 c - 15)}{3 c^{2} - 12}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $3$ out of $3 c^{2} - 12$ .

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Step 2.1.1

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

$\frac{2 (3 c^{2} - 2 c - 15)}{3 (c^{2}) - 12}$

Step 2.1.2

Factor $3$ out of $- 12$ .

$\frac{2 (3 c^{2} - 2 c - 15)}{3 c^{2} + 3 \cdot - 4}$

Step 2.1.3

Factor $3$ out of $3 c^{2} + 3 \cdot - 4$ .

$\frac{2 (3 c^{2} - 2 c - 15)}{3 (c^{2} - 4)}$

Step 2.2

Rewrite $4$ as $2^{2}$ .

$\frac{2 (3 c^{2} - 2 c - 15)}{3 (c^{2} - 2^{2})}$

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 $a = c$ and $b = 2$ .

$\frac{2 (3 c^{2} - 2 c - 15)}{3 (c + 2) (c - 2)}$