Pre-Algebra Examples

$\frac{6}{x^{2} + 4 x} + \frac{3}{2 x + 8}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

$\frac{6}{x \cdot x + 4 x} + \frac{3}{2 x + 8}$

Step 1.1.2

Factor $x$ out of $4 x$ .

$\frac{6}{x \cdot x + x \cdot 4} + \frac{3}{2 x + 8}$

Step 1.1.3

Factor $x$ out of $x \cdot x + x \cdot 4$ .

$\frac{6}{x (x + 4)} + \frac{3}{2 x + 8}$

Step 1.2

Factor $2$ out of $2 x + 8$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

$\frac{6}{x (x + 4)} + \frac{3}{2 (x) + 8}$

Step 1.2.2

Factor $2$ out of $8$ .

$\frac{6}{x (x + 4)} + \frac{3}{2 x + 2 \cdot 4}$

Step 1.2.3

Factor $2$ out of $2 x + 2 \cdot 4$ .

$\frac{6}{x (x + 4)} + \frac{3}{2 (x + 4)}$

Step 2

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

$\frac{6}{x (x + 4)} \cdot \frac{2}{2} + \frac{3}{2 (x + 4)}$

Step 3

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

$\frac{6}{x (x + 4)} \cdot \frac{2}{2} + \frac{3}{2 (x + 4)} \cdot \frac{x}{x}$

Step 4

Write each expression with a common denominator of $x (x + 4) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{6 \cdot 2}{x (x + 4) \cdot 2} + \frac{3}{2 (x + 4)} \cdot \frac{x}{x}$

Step 4.2

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

$\frac{6 \cdot 2}{x (x + 4) \cdot 2} + \frac{3 x}{2 (x + 4) x}$

Step 4.3

Reorder the factors of $x (x + 4) \cdot 2$ .

$\frac{6 \cdot 2}{2 x (x + 4)} + \frac{3 x}{2 (x + 4) x}$

Step 4.4

Reorder the factors of $2 (x + 4) x$ .

$\frac{6 \cdot 2}{2 x (x + 4)} + \frac{3 x}{2 x (x + 4)}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 \cdot 2 + 3 x}{2 x (x + 4)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $3$ out of $6 \cdot 2 + 3 x$ .

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Step 6.1.1

Factor $3$ out of $6 \cdot 2$ .

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

Step 6.1.2

Factor $3$ out of $3 x$ .

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

Step 6.1.3

Factor $3$ out of $3 (2 \cdot 2) + 3 (x)$ .

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

Step 6.2

Multiply $2$ by $2$ .

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

Step 7

Cancel the common factor of $4 + x$ and $x + 4$ .

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Step 7.1

Reorder terms.

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

$\frac{3}{2 x}$