Pre-Algebra Examples

$\frac{5 x}{2 x + 8} + \frac{3 x - 1}{x + 4}$

Step 1

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

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{5 x}{2 (x) + 8} + \frac{3 x - 1}{x + 4}$

Step 1.2

Factor $2$ out of $8$ .

$\frac{5 x}{2 x + 2 \cdot 4} + \frac{3 x - 1}{x + 4}$

Step 1.3

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

$\frac{5 x}{2 (x + 4)} + \frac{3 x - 1}{x + 4}$

Step 2

To write $\frac{3 x - 1}{x + 4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{2 (x + 4)} + \frac{3 x - 1}{x + 4} \cdot \frac{2}{2}$

Step 3

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

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Step 3.1

Multiply $\frac{3 x - 1}{x + 4}$ by $\frac{2}{2}$ .

$\frac{5 x}{2 (x + 4)} + \frac{(3 x - 1) \cdot 2}{(x + 4) \cdot 2}$

Step 3.2

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

$\frac{5 x}{2 (x + 4)} + \frac{(3 x - 1) \cdot 2}{2 (x + 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 x + (3 x - 1) \cdot 2}{2 (x + 4)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{5 x + 3 x \cdot 2 - 1 \cdot 2}{2 (x + 4)}$

Step 5.2

Multiply $2$ by $3$ .

$\frac{5 x + 6 x - 1 \cdot 2}{2 (x + 4)}$

Step 5.3

Multiply $- 1$ by $2$ .

$\frac{5 x + 6 x - 2}{2 (x + 4)}$

Step 5.4

Add $5 x$ and $6 x$ .

$\frac{11 x - 2}{2 (x + 4)}$