# How do you simplify and find the restrictions for 3/(x-4)-7?

##### 1 Answer
Aug 16, 2017

Restriction: $\textcolor{red}{x \ne 4}$
Simplification (maybe): $\textcolor{b l u e}{\frac{31 - 7 x}{x - 4}}$

#### Explanation:

Since division by $0$ is undefined.
$x - 4 \ne 0 \textcolor{w h i t e}{\text{xxx")rarrcolor(white)("xxx}} x \ne 4$

What is considered a "simplification" is more problematic.
Here is one possibility:
$\textcolor{w h i t e}{\text{XXX}} \frac{3}{x - 4} - 7$

$\textcolor{w h i t e}{\text{XXXXXX}} = \frac{3}{x - 4} - \frac{7 \left(x - 4\right)}{x - 4}$

$\textcolor{w h i t e}{\text{XXXXXX}} = \frac{3}{x - 4} - \frac{7 x - 28}{4}$

$\textcolor{w h i t e}{\text{XXXXXX}} = \frac{3 - 7 x + 28}{x - 4}$

$\textcolor{w h i t e}{\text{XXXXXX}} = \frac{31 - 7 x}{x - 4}$