Algebra Examples

$\frac{- 4 x^{3} - 8 x^{2} - 4 x - 8}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1

Cancel the common factor of $- 4 x^{3} - 8 x^{2} - 4 x - 8$ and $- 12 x^{3} - 12 x^{2} - 12 x - 12$ .

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Step 1.1

Factor $4$ out of $- 4 x^{3}$ .

$\frac{4 (- x^{3}) - 8 x^{2} - 4 x - 8}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1.2

Factor $4$ out of $- 8 x^{2}$ .

$\frac{4 (- x^{3}) + 4 (- 2 x^{2}) - 4 x - 8}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1.3

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

$\frac{4 (- x^{3} - 2 x^{2}) - 4 x - 8}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1.4

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

$\frac{4 (- x^{3} - 2 x^{2}) + 4 (- x) - 8}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1.5

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

$\frac{4 (- x^{3} - 2 x^{2} - x) - 8}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1.6

Factor $4$ out of $- 8$ .

$\frac{4 (- x^{3} - 2 x^{2} - x) + 4 (- 2)}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1.7

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

$\frac{4 (- x^{3} - 2 x^{2} - x - 2)}{- 12 x^{3} - 12 x^{2} - 12 x - 12}$

Step 1.8

Cancel the common factors.

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Step 1.8.1

Factor $4$ out of $- 12 x^{3}$ .

$\frac{4 (- x^{3} - 2 x^{2} - x - 2)}{4 (- 3 x^{3}) - 12 x^{2} - 12 x - 12}$

Step 1.8.2

Factor $4$ out of $- 12 x^{2}$ .

$\frac{4 (- x^{3} - 2 x^{2} - x - 2)}{4 (- 3 x^{3}) + 4 (- 3 x^{2}) - 12 x - 12}$

Step 1.8.3

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

$\frac{4 (- x^{3} - 2 x^{2} - x - 2)}{4 (- 3 x^{3} - 3 x^{2}) - 12 x - 12}$

Step 1.8.4

Factor $4$ out of $- 12 x$ .

$\frac{4 (- x^{3} - 2 x^{2} - x - 2)}{4 (- 3 x^{3} - 3 x^{2}) + 4 (- 3 x) - 12}$

Step 1.8.5

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

$\frac{4 (- x^{3} - 2 x^{2} - x - 2)}{4 (- 3 x^{3} - 3 x^{2} - 3 x) - 12}$

Step 1.8.6

Factor $4$ out of $- 12$ .

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

Step 1.8.7

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

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

Step 1.8.8

Cancel the common factor.

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

Step 1.8.9

Rewrite the expression.

$\frac{- x^{3} - 2 x^{2} - x - 2}{- 3 x^{3} - 3 x^{2} - 3 x - 3}$

Step 2

Simplify the numerator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

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

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{x^{2} (- x - 2) + 1 (- x - 2)}{- 3 x^{3} - 3 x^{2} - 3 x - 3}$

Step 2.2

Factor the polynomial by factoring out the greatest common factor, $- x - 2$ .

$\frac{(- x - 2) (x^{2} + 1)}{- 3 x^{3} - 3 x^{2} - 3 x - 3}$

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

Factor $3$ out of $- 3 x^{3}$ .

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x^{3}) - 3 x^{2} - 3 x - 3}$

Step 3.1.2

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

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x^{3}) + 3 (- x^{2}) - 3 x - 3}$

Step 3.1.3

Factor $3$ out of $- 3 x$ .

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x^{3}) + 3 (- x^{2}) + 3 (- x) - 3}$

Step 3.1.4

Factor $3$ out of $- 3$ .

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x^{3}) + 3 (- x^{2}) + 3 (- x) + 3 (- 1)}$

Step 3.1.5

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

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x^{3} - x^{2}) + 3 (- x) + 3 (- 1)}$

Step 3.1.6

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

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x^{3} - x^{2} - x) + 3 (- 1)}$

Step 3.1.7

Factor $3$ out of $3 (- x^{3} - x^{2} - x) + 3 (- 1)$ .

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x^{3} - x^{2} - x - 1)}$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$\frac{(- x - 2) (x^{2} + 1)}{3 ((- x^{3} - x^{2}) - x - 1)}$

Step 3.2.2

Factor out the greatest common factor (GCF) from each group.

$\frac{(- x - 2) (x^{2} + 1)}{3 (x^{2} (- x - 1) + 1 (- x - 1))}$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $- x - 1$ .

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x - 1) (x^{2} + 1)}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x^{2} + 1$ .

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Step 4.1.1

Cancel the common factor.

$\frac{(- x - 2) (x^{2} + 1)}{3 (- x - 1) (x^{2} + 1)}$

Step 4.1.2

Rewrite the expression.

$\frac{- x - 2}{3 (- x - 1)}$

Step 4.2

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

$\frac{- (x) - 2}{3 (- x - 1)}$

Step 4.3

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (x) - 1 (2)}{3 (- x - 1)}$

Step 4.4

Factor $- 1$ out of $- (x) - 1 (2)$ .

$\frac{- (x + 2)}{3 (- x - 1)}$

Step 4.5

Rewrite $- (x + 2)$ as $- 1 (x + 2)$ .

$\frac{- 1 (x + 2)}{3 (- x - 1)}$

Step 4.6

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

$\frac{- 1 (x + 2)}{3 (- (x) - 1)}$

Step 4.7

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

$\frac{- 1 (x + 2)}{3 (- (x) - 1 (1))}$

Step 4.8

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

$\frac{- 1 (x + 2)}{3 (- (x + 1))}$

Step 4.9

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

$\frac{- 1 (x + 2)}{3 (- 1 (x + 1))}$

Step 4.10

Cancel the common factor.

$\frac{- 1 (x + 2)}{3 (- 1 (x + 1))}$

Step 4.11

Rewrite the expression.

$\frac{x + 2}{3 (x + 1)}$