Algebra Examples

$\frac{8}{- 4 {(x + 3)}^{2} + 5 (x + 3)}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Factor $x + 3$ out of $- 4 {(x + 3)}^{2} + 5 (x + 3)$ .

Tap for more steps...

Step 1.1.1

Factor $x + 3$ out of $- 4 {(x + 3)}^{2}$ .

$\frac{8}{(x + 3) (- 4 (x + 3)) + 5 (x + 3)}$

Step 1.1.2

Factor $x + 3$ out of $5 (x + 3)$ .

$\frac{8}{(x + 3) (- 4 (x + 3)) + (x + 3) \cdot 5}$

Step 1.1.3

Factor $x + 3$ out of $(x + 3) (- 4 (x + 3)) + (x + 3) \cdot 5$ .

$\frac{8}{(x + 3) (- 4 (x + 3) + 5)}$

Step 1.2

Apply the distributive property.

$\frac{8}{(x + 3) (- 4 x - 4 \cdot 3 + 5)}$

Step 1.3

Multiply $- 4$ by $3$ .

$\frac{8}{(x + 3) (- 4 x - 12 + 5)}$

Step 1.4

Add $- 12$ and $5$ .

$\frac{8}{(x + 3) (- 4 x - 7)}$

Step 2

Simplify with factoring out.

Tap for more steps...

Step 2.1

Factor $- 1$ out of $- 4 x$ .

$\frac{8}{(x + 3) (- (4 x) - 7)}$

Step 2.2

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{8}{(x + 3) (- (4 x) - 1 (7))}$

Step 2.3

Factor $- 1$ out of $- (4 x) - 1 (7)$ .

$\frac{8}{(x + 3) (- (4 x + 7))}$

Step 2.4

Rewrite negatives.

Tap for more steps...

Step 2.4.1

Rewrite $- (4 x + 7)$ as $- 1 (4 x + 7)$ .

$\frac{8}{(x + 3) (- 1 (4 x + 7))}$

Step 2.4.2

Move the negative in front of the fraction.

$- \frac{8}{(x + 3) (4 x + 7)}$