Pre-Algebra Examples

$\frac{2}{4 x + 12} + \frac{7}{x + 3}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ and $4 x + 12$ .

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Step 1.1.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{4 x + 12} + \frac{7}{x + 3}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $4 x$ .

$\frac{2 (1)}{2 (2 x) + 12} + \frac{7}{x + 3}$

Step 1.1.2.2

Factor $2$ out of $12$ .

$\frac{2 \cdot 1}{2 (2 x) + 2 \cdot 6} + \frac{7}{x + 3}$

Step 1.1.2.3

Factor $2$ out of $2 (2 x) + 2 (6)$ .

$\frac{2 (1)}{2 (2 x + 6)} + \frac{7}{x + 3}$

Step 1.1.2.4

Cancel the common factor.

$\frac{2 \cdot 1}{2 (2 x + 6)} + \frac{7}{x + 3}$

Step 1.1.2.5

Rewrite the expression.

$\frac{1}{2 x + 6} + \frac{7}{x + 3}$

Step 1.2

Factor $2$ out of $2 x + 6$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2 (x) + 6} + \frac{7}{x + 3}$

Step 1.2.2

Factor $2$ out of $6$ .

$\frac{1}{2 x + 2 \cdot 3} + \frac{7}{x + 3}$

Step 1.2.3

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

$\frac{1}{2 (x + 3)} + \frac{7}{x + 3}$

Step 2

To write $\frac{7}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2 (x + 3)} + \frac{7}{x + 3} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $2 (x + 3)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{x + 3}$ by $\frac{2}{2}$ .

$\frac{1}{2 (x + 3)} + \frac{7 \cdot 2}{(x + 3) \cdot 2}$

Step 3.2

Reorder the factors of $(x + 3) \cdot 2$ .

$\frac{1}{2 (x + 3)} + \frac{7 \cdot 2}{2 (x + 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 7 \cdot 2}{2 (x + 3)}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $2$ .

$\frac{1 + 14}{2 (x + 3)}$

Step 5.2

Add $1$ and $14$ .

$\frac{15}{2 (x + 3)}$