Algebra Examples

$\frac{x}{3 x + 12} - \frac{x + 1}{x + 4}$

Step 1

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

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Step 1.1

Factor $3$ out of $3 x$ .

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

Step 1.2

Factor $3$ out of $12$ .

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

Step 1.3

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $3 (x + 4)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Reorder the factors of $(x + 4) \cdot 3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $- 1$ by $1$ .

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

Step 5.3

Apply the distributive property.

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

Step 5.4

Multiply $3$ by $- 1$ .

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

Step 5.5

Multiply $- 1$ by $3$ .

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

Step 5.6

Subtract $3 x$ from $x$ .

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

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- 2 x$ .

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

Step 6.2

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 6.3

Factor $- 1$ out of $- (2 x) - 1 (3)$ .

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

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (2 x + 3)$ as $- 1 (2 x + 3)$ .

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

Step 6.4.2

Move the negative in front of the fraction.

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