Pre-Algebra Examples

$\frac{6 x^{2} + 6 x^{3} - 6 x - 6}{3 x + 3}$

Step 1

Cancel the common factor of $6 x^{2} + 6 x^{3} - 6 x - 6$ and $3 x + 3$ .

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Step 1.1

Factor $3$ out of $6 x^{2}$ .

$\frac{3 (2 x^{2}) + 6 x^{3} - 6 x - 6}{3 x + 3}$

Step 1.2

Factor $3$ out of $6 x^{3}$ .

$\frac{3 (2 x^{2}) + 3 (2 x^{3}) - 6 x - 6}{3 x + 3}$

Step 1.3

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

$\frac{3 (2 x^{2} + 2 x^{3}) - 6 x - 6}{3 x + 3}$

Step 1.4

Factor $3$ out of $- 6 x$ .

$\frac{3 (2 x^{2} + 2 x^{3}) + 3 (- 2 x) - 6}{3 x + 3}$

Step 1.5

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

$\frac{3 (2 x^{2} + 2 x^{3} - 2 x) - 6}{3 x + 3}$

Step 1.6

Factor $3$ out of $- 6$ .

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

Step 1.7

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

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

Step 1.8

Cancel the common factors.

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Step 1.8.1

Factor $3$ out of $3 x$ .

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

Step 1.8.2

Factor $3$ out of $3$ .

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

Step 1.8.3

Factor $3$ out of $3 (x) + 3 (1)$ .

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

Step 1.8.4

Cancel the common factor.

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

Step 1.8.5

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

Factor $2$ out of $- 2 x$ .

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

Step 2.1.4

Factor $2$ out of $- 2$ .

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

Step 2.1.5

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

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

Step 2.1.6

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

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

Step 2.1.7

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

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

Step 2.2

Reorder terms.

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

Step 2.3

Factor out the greatest common factor from each group.

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Step 2.3.1

Group the first two terms and the last two terms.

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

Step 2.3.2

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

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

Step 2.4

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

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

Step 2.5

Rewrite $1$ as $1^{2}$ .

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

Step 2.6

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 $b = 1$ .

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

Step 2.7

Combine exponents.

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Step 2.7.1

Raise $x + 1$ to the power of $1$ .

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

Step 2.7.2

Raise $x + 1$ to the power of $1$ .

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

Step 2.7.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.7.4

Add $1$ and $1$ .

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $2 (x + 1) (x - 1)$ by $1$ .

$2 (x + 1) (x - 1)$

Step 4

Apply the distributive property.

$(2 x + 2 \cdot 1) (x - 1)$

Step 5

Multiply $2$ by $1$ .

$(2 x + 2) (x - 1)$

Step 6

Expand $(2 x + 2) (x - 1)$ using the FOIL Method.

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Step 6.1

Apply the distributive property.

$2 x (x - 1) + 2 (x - 1)$

Step 6.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 2 (x - 1)$

Step 6.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 2 x + 2 \cdot - 1$

Step 7

Simplify and combine like terms.

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Step 7.1

Simplify each term.

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Step 7.1.1

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

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Step 7.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 1 + 2 x + 2 \cdot - 1$

Step 7.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 1 + 2 x + 2 \cdot - 1$

Step 7.1.2

Multiply $- 1$ by $2$ .

$2 x^{2} - 2 x + 2 x + 2 \cdot - 1$

Step 7.1.3

Multiply $2$ by $- 1$ .

$2 x^{2} - 2 x + 2 x - 2$

Step 7.2

Add $- 2 x$ and $2 x$ .

$2 x^{2} + 0 - 2$

Step 7.3

Add $2 x^{2}$ and $0$ .

$2 x^{2} - 2$