Algebra Examples

$\frac{6}{x^{2} - 4} + \frac{3 x}{x - 2} + \frac{3}{x + 2} = 0$

Step 1

To write $\frac{6}{x^{2} - 4}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

$\frac{6}{x^{2} - 4} \cdot \frac{x - 2}{x - 2} + \frac{3 x}{x - 2} + \frac{3}{x + 2} = 0$

Step 2

To write $\frac{3 x}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{x^{2} - 4}{x^{2} - 4}$ .

$\frac{6}{x^{2} - 4} \cdot \frac{x - 2}{x - 2} + \frac{3 x}{x - 2} \cdot \frac{x^{2} - 4}{x^{2} - 4} + \frac{3}{x + 2} = 0$

Step 3

Write each expression with a common denominator of $(x^{2} - 4) (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{x^{2} - 4}$ by $\frac{x - 2}{x - 2}$ .

$\frac{6 (x - 2)}{(x^{2} - 4) (x - 2)} + \frac{3 x}{x - 2} \cdot \frac{x^{2} - 4}{x^{2} - 4} + \frac{3}{x + 2} = 0$

Step 3.2

Multiply $\frac{3 x}{x - 2}$ by $\frac{x^{2} - 4}{x^{2} - 4}$ .

$\frac{6 (x - 2)}{(x^{2} - 4) (x - 2)} + \frac{3 x (x^{2} - 4)}{(x - 2) (x^{2} - 4)} + \frac{3}{x + 2} = 0$

Step 3.3

Reorder the factors of $(x^{2} - 4) (x - 2)$ .

$\frac{6 (x - 2)}{(x - 2) (x^{2} - 4)} + \frac{3 x (x^{2} - 4)}{(x - 2) (x^{2} - 4)} + \frac{3}{x + 2} = 0$

Step 4

Combine the numerators over the common denominator.

$\frac{6 (x - 2) + 3 x (x^{2} - 4)}{(x - 2) (x^{2} - 4)} + \frac{3}{x + 2} = 0$

Step 5

To write $\frac{6 (x - 2) + 3 x (x^{2} - 4)}{(x - 2) (x^{2} - 4)}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$\frac{6 (x - 2) + 3 x (x^{2} - 4)}{(x - 2) (x^{2} - 4)} \cdot \frac{x + 2}{x + 2} + \frac{3}{x + 2} = 0$

Step 6

To write $\frac{3}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{(x - 2) (x^{2} - 4)}{(x - 2) (x^{2} - 4)}$ .

$\frac{6 (x - 2) + 3 x (x^{2} - 4)}{(x - 2) (x^{2} - 4)} \cdot \frac{x + 2}{x + 2} + \frac{3}{x + 2} \cdot \frac{(x - 2) (x^{2} - 4)}{(x - 2) (x^{2} - 4)} = 0$

Step 7

Write each expression with a common denominator of $(x - 2) (x^{2} - 4) (x + 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{6 (x - 2) + 3 x (x^{2} - 4)}{(x - 2) (x^{2} - 4)}$ by $\frac{x + 2}{x + 2}$ .

$\frac{(6 (x - 2) + 3 x (x^{2} - 4)) (x + 2)}{(x - 2) (x^{2} - 4) (x + 2)} + \frac{3}{x + 2} \cdot \frac{(x - 2) (x^{2} - 4)}{(x - 2) (x^{2} - 4)} = 0$

Step 7.2

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

$\frac{(6 (x - 2) + 3 x (x^{2} - 4)) (x + 2)}{(x - 2) (x^{2} - 4) (x + 2)} + \frac{3 ((x - 2) (x^{2} - 4))}{(x + 2) ((x - 2) (x^{2} - 4))} = 0$

Step 7.3

Reorder the factors of $(x - 2) (x^{2} - 4) (x + 2)$ .

$\frac{(6 (x - 2) + 3 x (x^{2} - 4)) (x + 2)}{(x + 2) (x - 2) (x^{2} - 4)} + \frac{3 ((x - 2) (x^{2} - 4))}{(x + 2) ((x - 2) (x^{2} - 4))} = 0$

Step 7.4

Reorder the factors of $(x + 2) ((x - 2) (x^{2} - 4))$ .

$\frac{(6 (x - 2) + 3 x (x^{2} - 4)) (x + 2)}{(x + 2) (x - 2) (x^{2} - 4)} + \frac{3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 8

Combine the numerators over the common denominator.

$\frac{(6 (x - 2) + 3 x (x^{2} - 4)) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9

Rewrite $\frac{(6 (x - 2) + 3 x (x^{2} - 4)) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)}$ in a factored form.

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Step 9.1

Simplify each term.

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Step 9.1.1

Apply the distributive property.

$\frac{(6 x + 6 \cdot - 2 + 3 x (x^{2} - 4)) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.1.2

Multiply $6$ by $- 2$ .

$\frac{(6 x - 12 + 3 x (x^{2} - 4)) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.1.3

Apply the distributive property.

$\frac{(6 x - 12 + 3 x \cdot x^{2} + 3 x \cdot - 4) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.1.4

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 9.1.4.1

Move $x^{2}$ .

$\frac{(6 x - 12 + 3 (x^{2} x) + 3 x \cdot - 4) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.1.4.2

Multiply $x^{2}$ by $x$ .

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Step 9.1.4.2.1

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

$\frac{(6 x - 12 + 3 (x^{2} x) + 3 x \cdot - 4) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.1.4.2.2

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

$\frac{(6 x - 12 + 3 x^{2 + 1} + 3 x \cdot - 4) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.1.4.3

Add $2$ and $1$ .

$\frac{(6 x - 12 + 3 x^{3} + 3 x \cdot - 4) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.1.5

Multiply $- 4$ by $3$ .

$\frac{(6 x - 12 + 3 x^{3} - 12 x) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.2

Subtract $12 x$ from $6 x$ .

$\frac{(- 6 x - 12 + 3 x^{3}) (x + 2) + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.3

Expand $(- 6 x - 12 + 3 x^{3}) (x + 2)$ by multiplying each term in the first expression by each term in the second expression.

$\frac{- 6 x \cdot x - 6 x \cdot 2 - 12 x - 12 \cdot 2 + 3 x^{3} x + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4

Simplify each term.

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Step 9.4.1

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

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Step 9.4.1.1

Move $x$ .

$\frac{- 6 (x \cdot x) - 6 x \cdot 2 - 12 x - 12 \cdot 2 + 3 x^{3} x + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.1.2

Multiply $x$ by $x$ .

$\frac{- 6 x^{2} - 6 x \cdot 2 - 12 x - 12 \cdot 2 + 3 x^{3} x + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.2

Multiply $2$ by $- 6$ .

$\frac{- 6 x^{2} - 12 x - 12 x - 12 \cdot 2 + 3 x^{3} x + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.3

Multiply $- 12$ by $2$ .

$\frac{- 6 x^{2} - 12 x - 12 x - 24 + 3 x^{3} x + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.4

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 9.4.4.1

Move $x$ .

$\frac{- 6 x^{2} - 12 x - 12 x - 24 + 3 (x \cdot x^{3}) + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.4.2

Multiply $x$ by $x^{3}$ .

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Step 9.4.4.2.1

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

$\frac{- 6 x^{2} - 12 x - 12 x - 24 + 3 (x \cdot x^{3}) + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.4.2.2

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

$\frac{- 6 x^{2} - 12 x - 12 x - 24 + 3 x^{1 + 3} + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.4.3

Add $1$ and $3$ .

$\frac{- 6 x^{2} - 12 x - 12 x - 24 + 3 x^{4} + 3 x^{3} \cdot 2 + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.4.5

Multiply $2$ by $3$ .

$\frac{- 6 x^{2} - 12 x - 12 x - 24 + 3 x^{4} + 6 x^{3} + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.5

Subtract $12 x$ from $- 12 x$ .

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 ((x - 2) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.6

Expand $(x - 2) (x^{2} - 4)$ using the FOIL Method.

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Step 9.6.1

Apply the distributive property.

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x (x^{2} - 4) - 2 (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.6.2

Apply the distributive property.

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x \cdot x^{2} + x \cdot - 4 - 2 (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.6.3

Apply the distributive property.

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x \cdot x^{2} + x \cdot - 4 - 2 x^{2} - 2 \cdot - 4)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.7

Simplify each term.

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Step 9.7.1

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 9.7.1.1

Multiply $x$ by $x^{2}$ .

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Step 9.7.1.1.1

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

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x \cdot x^{2} + x \cdot - 4 - 2 x^{2} - 2 \cdot - 4)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.7.1.1.2

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

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x^{1 + 2} + x \cdot - 4 - 2 x^{2} - 2 \cdot - 4)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.7.1.2

Add $1$ and $2$ .

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x^{3} + x \cdot - 4 - 2 x^{2} - 2 \cdot - 4)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.7.2

Move $- 4$ to the left of $x$ .

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x^{3} - 4 x - 2 x^{2} - 2 \cdot - 4)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.7.3

Multiply $- 2$ by $- 4$ .

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 (x^{3} - 4 x - 2 x^{2} + 8)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.8

Apply the distributive property.

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 x^{3} + 3 (- 4 x) + 3 (- 2 x^{2}) + 3 \cdot 8}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.9

Simplify.

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Step 9.9.1

Multiply $- 4$ by $3$ .

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 x^{3} - 12 x + 3 (- 2 x^{2}) + 3 \cdot 8}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.9.2

Multiply $- 2$ by $3$ .

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 x^{3} - 12 x - 6 x^{2} + 3 \cdot 8}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.9.3

Multiply $3$ by $8$ .

$\frac{- 6 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 x^{3} - 12 x - 6 x^{2} + 24}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.10

Subtract $6 x^{2}$ from $- 6 x^{2}$ .

$\frac{- 12 x^{2} - 24 x - 24 + 3 x^{4} + 6 x^{3} + 3 x^{3} - 12 x + 24}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.11

Subtract $12 x$ from $- 24 x$ .

$\frac{- 12 x^{2} - 24 + 3 x^{4} + 6 x^{3} + 3 x^{3} - 36 x + 24}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.12

Add $- 24$ and $24$ .

$\frac{- 12 x^{2} + 3 x^{4} + 6 x^{3} + 3 x^{3} - 36 x + 0}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.13

Add $- 12 x^{2} + 3 x^{4} + 6 x^{3} + 3 x^{3} - 36 x$ and $0$ .

$\frac{- 12 x^{2} + 3 x^{4} + 6 x^{3} + 3 x^{3} - 36 x}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.14

Add $6 x^{3}$ and $3 x^{3}$ .

$\frac{- 12 x^{2} + 3 x^{4} + 9 x^{3} - 36 x}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.15

Reorder terms.

$\frac{3 x^{4} + 9 x^{3} - 12 x^{2} - 36 x}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16

Rewrite $3 x^{4} + 9 x^{3} - 12 x^{2} - 36 x$ in a factored form.

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Step 9.16.1

Factor $3 x$ out of $3 x^{4} + 9 x^{3} - 12 x^{2} - 36 x$ .

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Step 9.16.1.1

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

$\frac{3 x (x^{3}) + 9 x^{3} - 12 x^{2} - 36 x}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.1.2

Factor $3 x$ out of $9 x^{3}$ .

$\frac{3 x (x^{3}) + 3 x (3 x^{2}) - 12 x^{2} - 36 x}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.1.3

Factor $3 x$ out of $- 12 x^{2}$ .

$\frac{3 x (x^{3}) + 3 x (3 x^{2}) + 3 x (- 4 x) - 36 x}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.1.4

Factor $3 x$ out of $- 36 x$ .

$\frac{3 x (x^{3}) + 3 x (3 x^{2}) + 3 x (- 4 x) + 3 x (- 12)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.1.5

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

$\frac{3 x (x^{3} + 3 x^{2}) + 3 x (- 4 x) + 3 x (- 12)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.1.6

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

$\frac{3 x (x^{3} + 3 x^{2} - 4 x) + 3 x (- 12)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.1.7

Factor $3 x$ out of $3 x (x^{3} + 3 x^{2} - 4 x) + 3 x (- 12)$ .

$\frac{3 x (x^{3} + 3 x^{2} - 4 x - 12)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.2

Factor out the greatest common factor from each group.

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Step 9.16.2.1

Group the first two terms and the last two terms.

$\frac{3 x ((x^{3} + 3 x^{2}) - 4 x - 12)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.2.2

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

$\frac{3 x (x^{2} (x + 3) - 4 (x + 3))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.3

Factor the polynomial by factoring out the greatest common factor, $x + 3$ .

$\frac{3 x ((x + 3) (x^{2} - 4))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.4

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

$\frac{3 x ((x + 3) (x^{2} - 2^{2}))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.5

Factor.

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Step 9.16.5.1

Factor.

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Step 9.16.5.1.1

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 $b = 2$ .

$\frac{3 x ((x + 3) ((x + 2) (x - 2)))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.5.1.2

Remove unnecessary parentheses.

$\frac{3 x ((x + 3) (x + 2) (x - 2))}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.16.5.2

Remove unnecessary parentheses.

$\frac{3 x (x + 3) (x + 2) (x - 2)}{(x + 2) (x - 2) (x^{2} - 4)} = 0$

Step 9.17

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

$\frac{3 x (x + 3) (x + 2) (x - 2)}{(x + 2) (x - 2) (x^{2} - 2^{2})} = 0$

Step 9.18

Factor.

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Step 9.18.1

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 $b = 2$ .

$\frac{3 x (x + 3) (x + 2) (x - 2)}{(x + 2) (x - 2) ((x + 2) (x - 2))} = 0$

Step 9.18.2

Remove unnecessary parentheses.

$\frac{3 x (x + 3) (x + 2) (x - 2)}{(x + 2) (x - 2) (x + 2) (x - 2)} = 0$

Step 9.19

Combine exponents.

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Step 9.19.1

Raise $x + 2$ to the power of $1$ .

$\frac{3 x (x + 3) (x + 2) (x - 2)}{(x + 2) (x + 2) (x - 2) (x - 2)} = 0$

Step 9.19.2

Raise $x + 2$ to the power of $1$ .

$\frac{3 x (x + 3) (x + 2) (x - 2)}{(x + 2) (x + 2) (x - 2) (x - 2)} = 0$

Step 9.19.3

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

$\frac{3 x (x + 3) (x + 2) (x - 2)}{{(x + 2)}^{1 + 1} (x - 2) (x - 2)} = 0$

Step 9.19.4

Add $1$ and $1$ .

$\frac{3 x (x + 3) (x + 2) (x - 2)}{{(x + 2)}^{2} (x - 2) (x - 2)} = 0$

Step 9.19.5

Raise $x - 2$ to the power of $1$ .

$\frac{3 x (x + 3) (x + 2) (x - 2)}{{(x + 2)}^{2} ((x - 2) (x - 2))} = 0$

Step 9.19.6

Raise $x - 2$ to the power of $1$ .

$\frac{3 x (x + 3) (x + 2) (x - 2)}{{(x + 2)}^{2} ((x - 2) (x - 2))} = 0$

Step 9.19.7

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

$\frac{3 x (x + 3) (x + 2) (x - 2)}{{(x + 2)}^{2} {(x - 2)}^{1 + 1}} = 0$

Step 9.19.8

Add $1$ and $1$ .

$\frac{3 x (x + 3) (x + 2) (x - 2)}{{(x + 2)}^{2} {(x - 2)}^{2}} = 0$

Step 9.20

Reduce the expression $\frac{3 x (x + 3) (x + 2) (x - 2)}{{(x + 2)}^{2} {(x - 2)}^{2}}$ by cancelling the common factors.

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Step 9.20.1

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

$\frac{(x + 2) (3 x (x + 3) (x - 2))}{{(x + 2)}^{2} {(x - 2)}^{2}} = 0$

Step 9.20.2

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

$\frac{(x + 2) (3 x (x + 3) (x - 2))}{(x + 2) ((x + 2) {(x - 2)}^{2})} = 0$

Step 9.20.3

Cancel the common factor.

$\frac{(x + 2) (3 x (x + 3) (x - 2))}{(x + 2) ((x + 2) {(x - 2)}^{2})} = 0$

Step 9.20.4

Rewrite the expression.

$\frac{3 x (x + 3) (x - 2)}{(x + 2) {(x - 2)}^{2}} = 0$

Step 10

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

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Step 10.1

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

$\frac{(x - 2) (3 x (x + 3))}{(x + 2) {(x - 2)}^{2}} = 0$

Step 10.2

Cancel the common factors.

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Step 10.2.1

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

$\frac{(x - 2) (3 x (x + 3))}{(x - 2) ((x + 2) (x - 2))} = 0$

Step 10.2.2

Cancel the common factor.

$\frac{(x - 2) (3 x (x + 3))}{(x - 2) ((x + 2) (x - 2))} = 0$

Step 10.2.3

Rewrite the expression.

$\frac{3 x (x + 3)}{(x + 2) (x - 2)} = 0$

Step 11

Set the numerator equal to zero.

$3 x (x + 3) = 0$

Step 12

Solve the equation for $x$ .

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Step 12.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 3 = 0$

Step 12.2

Set $x$ equal to $0$ .

$x = 0$

Step 12.3

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 12.3.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 12.3.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 12.4

The final solution is all the values that make $3 x (x + 3) = 0$ true.

$x = 0, - 3$