Algebra Examples

$\frac{3}{p + 4} + \frac{2 p + 32}{p^{2} - 16}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Factor $2$ out of $2 p + 32$ .

Tap for more steps...

Step 1.1.1

Factor $2$ out of $2 p$ .

$\frac{3}{p + 4} + \frac{2 (p) + 32}{p^{2} - 16}$

Step 1.1.2

Factor $2$ out of $32$ .

$\frac{3}{p + 4} + \frac{2 p + 2 \cdot 16}{p^{2} - 16}$

Step 1.1.3

Factor $2$ out of $2 p + 2 \cdot 16$ .

$\frac{3}{p + 4} + \frac{2 (p + 16)}{p^{2} - 16}$

Step 1.2

Simplify the denominator.

Tap for more steps...

Step 1.2.1

Rewrite $16$ as $4^{2}$ .

$\frac{3}{p + 4} + \frac{2 (p + 16)}{p^{2} - 4^{2}}$

Step 1.2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = p$ and $b = 4$ .

$\frac{3}{p + 4} + \frac{2 (p + 16)}{(p + 4) (p - 4)}$

Step 2

To write $\frac{3}{p + 4}$ as a fraction with a common denominator, multiply by $\frac{p - 4}{p - 4}$ .

$\frac{3}{p + 4} \cdot \frac{p - 4}{p - 4} + \frac{2 (p + 16)}{(p + 4) (p - 4)}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

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

$\frac{3 (p - 4)}{(p + 4) (p - 4)} + \frac{2 (p + 16)}{(p + 4) (p - 4)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 (p - 4) + 2 (p + 16)}{(p + 4) (p - 4)}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Apply the distributive property.

$\frac{3 p + 3 \cdot - 4 + 2 (p + 16)}{(p + 4) (p - 4)}$

Step 4.2

Multiply $3$ by $- 4$ .

$\frac{3 p - 12 + 2 (p + 16)}{(p + 4) (p - 4)}$

Step 4.3

Apply the distributive property.

$\frac{3 p - 12 + 2 p + 2 \cdot 16}{(p + 4) (p - 4)}$

Step 4.4

Multiply $2$ by $16$ .

$\frac{3 p - 12 + 2 p + 32}{(p + 4) (p - 4)}$

Step 4.5

Add $3 p$ and $2 p$ .

$\frac{5 p - 12 + 32}{(p + 4) (p - 4)}$

Step 4.6

Add $- 12$ and $32$ .

$\frac{5 p + 20}{(p + 4) (p - 4)}$

Step 4.7

Factor $5$ out of $5 p + 20$ .

Tap for more steps...

Step 4.7.1

Factor $5$ out of $5 p$ .

$\frac{5 (p) + 20}{(p + 4) (p - 4)}$

Step 4.7.2

Factor $5$ out of $20$ .

$\frac{5 p + 5 \cdot 4}{(p + 4) (p - 4)}$

Step 4.7.3

Factor $5$ out of $5 p + 5 \cdot 4$ .

$\frac{5 (p + 4)}{(p + 4) (p - 4)}$

Step 5

Cancel the common factor of $p + 4$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{5 (p + 4)}{(p + 4) (p - 4)}$

Step 5.2

Rewrite the expression.

$\frac{5}{p - 4}$