Precalculus Examples

$\frac{4 x \cdot 2 x - (x^{2} + 9) \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 1

Rewrite using the commutative property of multiplication.

$\frac{4 \cdot 2 x \cdot x - (x^{2} + 9) \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $x$ .

$\frac{4 \cdot 2 (x \cdot x) - (x^{2} + 9) \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 2.2

Multiply $x$ by $x$ .

$\frac{4 \cdot 2 x^{2} - (x^{2} + 9) \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 3

Multiply $4$ by $2$ .

$\frac{8 x^{2} - (x^{2} + 9) \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 4

Apply the distributive property.

$\frac{8 x^{2} + (- x^{2} - 1 \cdot 9) \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 5

Multiply $- 1$ by $9$ .

$\frac{8 x^{2} + (- x^{2} - 9) \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 6

Apply the distributive property.

$\frac{8 x^{2} - x^{2} \cdot 4 - 9 \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 7

Multiply $4$ by $- 1$ .

$\frac{8 x^{2} - 4 x^{2} - 9 \cdot 4}{{(x^{2} + 9)}^{2}}$

Step 8

Multiply $- 9$ by $4$ .

$\frac{8 x^{2} - 4 x^{2} - 36}{{(x^{2} + 9)}^{2}}$

Step 9

Subtract $4 x^{2}$ from $8 x^{2}$ .

$\frac{4 x^{2} - 36}{{(x^{2} + 9)}^{2}}$

Step 10

Rewrite $4 x^{2} - 36$ in a factored form.

Tap for more steps...

Step 10.1

Factor $4$ out of $4 x^{2} - 36$ .

Tap for more steps...

Step 10.1.1

Factor $4$ out of $4 x^{2}$ .

$\frac{4 (x^{2}) - 36}{{(x^{2} + 9)}^{2}}$

Step 10.1.2

Factor $4$ out of $- 36$ .

$\frac{4 x^{2} + 4 \cdot - 9}{{(x^{2} + 9)}^{2}}$

Step 10.1.3

Factor $4$ out of $4 x^{2} + 4 \cdot - 9$ .

$\frac{4 (x^{2} - 9)}{{(x^{2} + 9)}^{2}}$

Step 10.2

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

$\frac{4 (x^{2} - 3^{2})}{{(x^{2} + 9)}^{2}}$

Step 10.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{4 (x + 3) (x - 3)}{{(x^{2} + 9)}^{2}}$