Simplify x/(2x+8)-(5x+1)/(x+4)

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

Step 1

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $8$ .

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

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

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

Step 2

To write $- \frac{5 x + 1}{x + 4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

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

Multiply $\frac{5 x + 1}{x + 4}$ by $\frac{2}{2}$ .

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

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Apply the distributive property.

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

Multiply $5$ by $- 1$ .

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

Multiply $- 1$ by $1$ .

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

Apply the distributive property.

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

Multiply $2$ by $- 5$ .

$\frac{x - 10 x - 1 \cdot 2}{2 (x + 4)}$

Multiply $- 1$ by $2$ .

$\frac{x - 10 x - 2}{2 (x + 4)}$

Subtract $10 x$ from $x$ .

$\frac{- 9 x - 2}{2 (x + 4)}$

Step 6

Simplify with factoring out.

Factor $- 1$ out of $- 9 x$ .

$\frac{- (9 x) - 2}{2 (x + 4)}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (9 x) - 1 (2)}{2 (x + 4)}$

Factor $- 1$ out of $- (9 x) - 1 (2)$ .

$\frac{- (9 x + 2)}{2 (x + 4)}$

Simplify the expression.

Rewrite $- (9 x + 2)$ as $- 1 (9 x + 2)$ .

$\frac{- 1 (9 x + 2)}{2 (x + 4)}$

Move the negative in front of the fraction.

$- \frac{9 x + 2}{2 (x + 4)}$

Simplify x/(2x+8)-(5x+1)/(x+4)

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