Solve by Factoring 1/(3x+9)-2/(x+3)=2

$\frac{1}{3 x + 9} - \frac{2}{x + 3} = 2$

Step 1

Subtract $2$ from both sides of the equation.

$\frac{1}{3 x + 9} - \frac{2}{x + 3} - 2 = 0$

Step 2

Simplify $\frac{1}{3 x + 9} - \frac{2}{x + 3} - 2$ .

Factor $3$ out of $3 x + 9$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3 (x) + 9} - \frac{2}{x + 3} - 2 = 0$

Factor $3$ out of $9$ .

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $3$ .

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

Subtract $6$ from $1$ .

$\frac{- 5}{3 (x + 3)} - 2 = 0$

Move the negative in front of the fraction.

$- \frac{5}{3 (x + 3)} - 2 = 0$

Step 3

Factor $- 1$ out of $- \frac{5}{3 (x + 3)} - 2$ .

Factor $- 1$ out of $- \frac{5}{3 (x + 3)}$ .

$- (\frac{5}{3 (x + 3)}) - 2 = 0$

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

$- (\frac{5}{3 (x + 3)}) - 1 \cdot 2 = 0$

Factor $- 1$ out of $- (\frac{5}{3 (x + 3)}) - 1 (2)$ .

$- (\frac{5}{3 (x + 3)} + 2) = 0$

Step 4

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

$- (\frac{5}{3 (x + 3)} + 2 \cdot \frac{3 (x + 3)}{3 (x + 3)}) = 0$

Step 5

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

$- (\frac{5}{3 (x + 3)} + \frac{2 (3 (x + 3))}{3 (x + 3)}) = 0$

Step 6

Combine the numerators over the common denominator.

$- \frac{5 + 2 (3 (x + 3))}{3 (x + 3)} = 0$

Step 7

Remove parentheses.

$- \frac{5 + 2 \cdot (3 (x + 3))}{3 (x + 3)} = 0$

Step 8

Simplify the numerator.

Multiply $2$ by $3$ .

$- \frac{5 + 6 (x + 3)}{3 (x + 3)} = 0$

Apply the distributive property.

$- \frac{5 + 6 x + 6 \cdot 3}{3 (x + 3)} = 0$

Multiply $6$ by $3$ .

$- \frac{5 + 6 x + 18}{3 (x + 3)} = 0$

Add $5$ and $18$ .

$- \frac{6 x + 23}{3 (x + 3)} = 0$

Step 9

Set the numerator equal to zero.

$6 x + 23 = 0$

Step 10

Solve the equation for $x$ .

Subtract $23$ from both sides of the equation.

$6 x = - 23$

Divide each term in $6 x = - 23$ by $6$ and simplify.

Divide each term in $6 x = - 23$ by $6$ .

$\frac{6 x}{6} = \frac{- 23}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 23}{6}$

Divide $x$ by $1$ .

$x = \frac{- 23}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{23}{6}$

Solve by Factoring 1/(3x+9)-2/(x+3)=2

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