Pre-Algebra Examples

$\frac{x + 5}{3 x + 12} - \frac{x - 4}{4 x + 16}$

Step 1

Simplify each term.

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Step 1.1

Factor $3$ out of $3 x + 12$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{x + 5}{3 (x) + 12} - \frac{x - 4}{4 x + 16}$

Step 1.1.2

Factor $3$ out of $12$ .

$\frac{x + 5}{3 x + 3 \cdot 4} - \frac{x - 4}{4 x + 16}$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot 4$ .

$\frac{x + 5}{3 (x + 4)} - \frac{x - 4}{4 x + 16}$

Step 1.2

Factor $4$ out of $4 x + 16$ .

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Step 1.2.1

Factor $4$ out of $4 x$ .

$\frac{x + 5}{3 (x + 4)} - \frac{x - 4}{4 (x) + 16}$

Step 1.2.2

Factor $4$ out of $16$ .

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

Step 1.2.3

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

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

Step 2

To write $\frac{x + 5}{3 (x + 4)}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $12 (x + 4)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x + 5}{3 (x + 4)}$ by $\frac{4}{4}$ .

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

Step 4.2

Multiply $4$ by $3$ .

$\frac{(x + 5) \cdot 4}{12 (x + 4)} - \frac{x - 4}{4 (x + 4)} \cdot \frac{3}{3}$

Step 4.3

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

$\frac{(x + 5) \cdot 4}{12 (x + 4)} - \frac{(x - 4) \cdot 3}{4 (x + 4) \cdot 3}$

Step 4.4

Multiply $3$ by $4$ .

$\frac{(x + 5) \cdot 4}{12 (x + 4)} - \frac{(x - 4) \cdot 3}{12 (x + 4)}$

Step 5

Combine the numerators over the common denominator.

$\frac{(x + 5) \cdot 4 - (x - 4) \cdot 3}{12 (x + 4)}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{x \cdot 4 + 5 \cdot 4 - (x - 4) \cdot 3}{12 (x + 4)}$

Step 6.2

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

$\frac{4 \cdot x + 5 \cdot 4 - (x - 4) \cdot 3}{12 (x + 4)}$

Step 6.3

Multiply $5$ by $4$ .

$\frac{4 \cdot x + 20 - (x - 4) \cdot 3}{12 (x + 4)}$

Step 6.4

Apply the distributive property.

$\frac{4 x + 20 + (- x - - 4) \cdot 3}{12 (x + 4)}$

Step 6.5

Multiply $- 1$ by $- 4$ .

$\frac{4 x + 20 + (- x + 4) \cdot 3}{12 (x + 4)}$

Step 6.6

Apply the distributive property.

$\frac{4 x + 20 - x \cdot 3 + 4 \cdot 3}{12 (x + 4)}$

Step 6.7

Multiply $3$ by $- 1$ .

$\frac{4 x + 20 - 3 x + 4 \cdot 3}{12 (x + 4)}$

Step 6.8

Multiply $4$ by $3$ .

$\frac{4 x + 20 - 3 x + 12}{12 (x + 4)}$

Step 6.9

Subtract $3 x$ from $4 x$ .

$\frac{x + 20 + 12}{12 (x + 4)}$

Step 6.10

Add $20$ and $12$ .

$\frac{x + 32}{12 (x + 4)}$