Solve by Factoring x/(2x+6)-1/(x+3)=1

$\frac{x}{2 x + 6} - \frac{1}{x + 3} = 1$

Step 1

Subtract $1$ from both sides of the equation.

$\frac{x}{2 x + 6} - \frac{1}{x + 3} - 1 = 0$

Step 2

Simplify $\frac{x}{2 x + 6} - \frac{1}{x + 3} - 1$ .

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

Factor $2$ out of $2 x$ .

$\frac{x}{2 (x) + 6} - \frac{1}{x + 3} - 1 = 0$

Factor $2$ out of $6$ .

$\frac{x}{2 x + 2 \cdot 3} - \frac{1}{x + 3} - 1 = 0$

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

$\frac{x}{2 (x + 3)} - \frac{1}{x + 3} - 1 = 0$

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

$\frac{x}{2 (x + 3)} - \frac{1}{x + 3} \cdot \frac{2}{2} - 1 = 0$

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

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

$\frac{x}{2 (x + 3)} - \frac{2}{(x + 3) \cdot 2} - 1 = 0$

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

$\frac{x}{2 (x + 3)} - \frac{2}{2 (x + 3)} - 1 = 0$

Combine the numerators over the common denominator.

$\frac{x - 2}{2 (x + 3)} - 1 = 0$

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

$\frac{x - 2}{2 (x + 3)} - 1 \cdot \frac{2 (x + 3)}{2 (x + 3)} = 0$

Combine $- 1$ and $\frac{2 (x + 3)}{2 (x + 3)}$ .

$\frac{x - 2}{2 (x + 3)} + \frac{- (2 (x + 3))}{2 (x + 3)} = 0$

Combine the numerators over the common denominator.

$\frac{x - 2 - (2 (x + 3))}{2 (x + 3)} = 0$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{x - 2 - 2 (x + 3)}{2 (x + 3)} = 0$

Apply the distributive property.

$\frac{x - 2 - 2 x - 2 \cdot 3}{2 (x + 3)} = 0$

Multiply $- 2$ by $3$ .

$\frac{x - 2 - 2 x - 6}{2 (x + 3)} = 0$

Subtract $2 x$ from $x$ .

$\frac{- x - 2 - 6}{2 (x + 3)} = 0$

Subtract $6$ from $- 2$ .

$\frac{- x - 8}{2 (x + 3)} = 0$

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

$\frac{- (x) - 8}{2 (x + 3)} = 0$

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{- (x) - 1 (8)}{2 (x + 3)} = 0$

Factor $- 1$ out of $- (x) - 1 (8)$ .

$\frac{- (x + 8)}{2 (x + 3)} = 0$

Rewrite $- (x + 8)$ as $- 1 (x + 8)$ .

$\frac{- 1 (x + 8)}{2 (x + 3)} = 0$

Move the negative in front of the fraction.

$- \frac{x + 8}{2 (x + 3)} = 0$

Step 3

Set the numerator equal to zero.

$x + 8 = 0$

Step 4

Subtract $8$ from both sides of the equation.

$x = - 8$

Solve by Factoring x/(2x+6)-1/(x+3)=1

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