Algebra Examples

$\frac{c^{2} + 4 c}{c^{2} - 4} \div \frac{3 c + 12}{c - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c^{2} + 4 c}{c^{2} - 4} \cdot \frac{c - 2}{3 c + 12}$

Step 2

Factor $c$ out of $c^{2} + 4 c$ .

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Step 2.1

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

$\frac{c \cdot c + 4 c}{c^{2} - 4} \cdot \frac{c - 2}{3 c + 12}$

Step 2.2

Factor $c$ out of $4 c$ .

$\frac{c \cdot c + c \cdot 4}{c^{2} - 4} \cdot \frac{c - 2}{3 c + 12}$

Step 2.3

Factor $c$ out of $c \cdot c + c \cdot 4$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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 $b = 2$ .

$\frac{c (c + 4)}{(c + 2) (c - 2)} \cdot \frac{c - 2}{3 c + 12}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $c - 2$ .

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Step 4.1.1

Factor $c - 2$ out of $(c + 2) (c - 2)$ .

$\frac{c (c + 4)}{(c - 2) (c + 2)} \cdot \frac{c - 2}{3 c + 12}$

Step 4.1.2

Cancel the common factor.

$\frac{c (c + 4)}{(c - 2) (c + 2)} \cdot \frac{c - 2}{3 c + 12}$

Step 4.1.3

Rewrite the expression.

$\frac{c (c + 4)}{c + 2} \cdot \frac{1}{3 c + 12}$

Step 4.2

Multiply $\frac{c (c + 4)}{c + 2}$ by $\frac{1}{3 c + 12}$ .

$\frac{c (c + 4)}{(c + 2) (3 c + 12)}$

Step 5

Factor $3$ out of $3 c + 12$ .

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Step 5.1

Factor $3$ out of $3 c$ .

$\frac{c (c + 4)}{(c + 2) (3 (c) + 12)}$

Step 5.2

Factor $3$ out of $12$ .

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

Step 5.3

Factor $3$ out of $3 c + 3 \cdot 4$ .

$\frac{c (c + 4)}{(c + 2) (3 (c + 4))}$

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

Step 6

Cancel the common factor of $c + 4$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{c}{(c + 2) \cdot 3}$

Step 7

Move $3$ to the left of $c + 2$ .

$\frac{c}{3 (c + 2)}$