# (x-9)/(x+4)=3?

## Math

##### 2 Answers
Apr 26, 2018

$x = - \frac{21}{2}$

#### Explanation:

$\frac{x - 9}{x + 4} = 3$ $/ \cdot \left(x + 4\right)$ to get rid of the fraction

$x - 9 = 3 \cdot \left(x + 4\right)$

$x - 9 = 3 x + 12$

$x - 3 x = 12 + 9$

$- 2 x = 21$ $/ \cdot \left(- 1\right)$

$2 x = - 21$

$x = - \frac{21}{2}$

Apr 26, 2018

$x = - \frac{21}{2}$

#### Explanation:

We must begin by adding the domain restriction $x \ne - 4$ because this would cause division by 0:

$\frac{x - 9}{x + 4} = 3 , x \ne - 4$

Now that we have assured that we are not inadvertently multiplying by 0, we can eliminate the denominator by multiplying both sides by $\left(x + 4\right)$:

$x - 9 = 3 \left(x + 4\right) , x \ne - 4$

Use the distributive property:

$x - 9 = 3 x + 12 , x \ne - 4$

Add $9 - 3 x$ to both sides:

$- 2 x = 21 , x \ne - 4$

We can drop the domain restriction because it is obvious that the solution will not violate it:

$- 2 x = 21$

Multiply both sides by $- \frac{1}{2}$:

$x = - \frac{21}{2}$