Trigonometry Examples

$\frac{a^{2} - 9}{a^{2} - 3 a} \cdot \frac{a^{2} + a}{a + 3}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

$\frac{a^{2} - 3^{2}}{a^{2} - 3 a} \cdot \frac{a^{2} + a}{a + 3}$

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 $a = a$ and $b = 3$ .

$\frac{(a + 3) (a - 3)}{a^{2} - 3 a} \cdot \frac{a^{2} + a}{a + 3}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

$\frac{(a + 3) (a - 3)}{a \cdot a - 3 a} \cdot \frac{a^{2} + a}{a + 3}$

Step 2.1.2

Factor $a$ out of $- 3 a$ .

$\frac{(a + 3) (a - 3)}{a \cdot a + a \cdot - 3} \cdot \frac{a^{2} + a}{a + 3}$

Step 2.1.3

Factor $a$ out of $a \cdot a + a \cdot - 3$ .

$\frac{(a + 3) (a - 3)}{a (a - 3)} \cdot \frac{a^{2} + a}{a + 3}$

Step 2.2

Factor $a$ out of $a^{2} + a$ .

Tap for more steps...

Step 2.2.1

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

$\frac{(a + 3) (a - 3)}{a (a - 3)} \cdot \frac{a \cdot a + a}{a + 3}$

Step 2.2.2

Raise $a$ to the power of $1$ .

$\frac{(a + 3) (a - 3)}{a (a - 3)} \cdot \frac{a \cdot a + a^{1}}{a + 3}$

Step 2.2.3

Factor $a$ out of $a^{1}$ .

$\frac{(a + 3) (a - 3)}{a (a - 3)} \cdot \frac{a \cdot a + a \cdot 1}{a + 3}$

Step 2.2.4

Factor $a$ out of $a \cdot a + a \cdot 1$ .

$\frac{(a + 3) (a - 3)}{a (a - 3)} \cdot \frac{a (a + 1)}{a + 3}$

Step 2.3

Cancel the common factor of $a + 3$ .

Tap for more steps...

Step 2.3.1

Cancel the common factor.

$\frac{(a + 3) (a - 3)}{a (a - 3)} \cdot \frac{a (a + 1)}{a + 3}$

Step 2.3.2

Rewrite the expression.

$\frac{a - 3}{a (a - 3)} \cdot (a (a + 1))$

Step 2.4

Cancel the common factor of $a$ .

Tap for more steps...

Step 2.4.1

Cancel the common factor.

$\frac{a - 3}{a (a - 3)} \cdot (a (a + 1))$

Step 2.4.2

Rewrite the expression.

$\frac{a - 3}{a - 3} \cdot (a + 1)$

Step 2.5

Cancel the common factor of $a - 3$ .

Tap for more steps...

Step 2.5.1

Cancel the common factor.

$\frac{a - 3}{a - 3} \cdot (a + 1)$

Step 2.5.2

Rewrite the expression.

$1 \cdot (a + 1)$

Step 2.6

Multiply $a + 1$ by $1$ .

$a + 1$