Basic Math Examples

$\frac{c^{2} - 9}{c + 1} \cdot \frac{4 c + 4}{c^{2} + 5 c + 6}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{c^{2} - 3^{2}}{c + 1} \cdot \frac{4 c + 4}{c^{2} + 5 c + 6}$

Step 1.2

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 $b = 3$ .

$\frac{(c + 3) (c - 3)}{c + 1} \cdot \frac{4 c + 4}{c^{2} + 5 c + 6}$

Step 2

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

Tap for more steps...

Step 2.1

Factor $4$ out of $4 c$ .

$\frac{(c + 3) (c - 3)}{c + 1} \cdot \frac{4 (c) + 4}{c^{2} + 5 c + 6}$

Step 2.2

Factor $4$ out of $4$ .

$\frac{(c + 3) (c - 3)}{c + 1} \cdot \frac{4 (c) + 4 (1)}{c^{2} + 5 c + 6}$

Step 2.3

Factor $4$ out of $4 (c) + 4 (1)$ .

$\frac{(c + 3) (c - 3)}{c + 1} \cdot \frac{4 (c + 1)}{c^{2} + 5 c + 6}$

Step 3

Factor $c^{2} + 5 c + 6$ using the AC method.

Tap for more steps...

Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $6$ and whose sum is $5$ .

$2, 3$

Step 3.2

Write the factored form using these integers.

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

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Cancel the common factor of $c + 3$ .

Tap for more steps...

Step 4.1.1

Factor $c + 3$ out of $(c + 2) (c + 3)$ .

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $c + 1$ .

Tap for more steps...

Step 4.2.1

Factor $c + 1$ out of $4 (c + 1)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.3

Multiply $c - 3$ by $\frac{4}{c + 2}$ .

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

Step 4.4

Move $4$ to the left of $c - 3$ .

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