# How do you simplify and find the restrictions for 1/(x+4) -2?

Jan 31, 2017

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

Restriction (excluded value) is: $x = - 4$

#### Explanation:

You are not allowed (undefined) to divide by 0 so $x + 4 \ne 0$
means that the excluded value is $x = - 4$

To solve this you need to 'force' the - 2 to be something over $x + 4$

color(green)(1/(x+4)-[2xxcolor(red)(1)]

But 1 = $\frac{x + 4}{x + 4}$

$\textcolor{g r e e n}{\frac{1}{x + 4} - \left[2 \times \textcolor{red}{\frac{x + 4}{x + 4}}\right]}$

$\textcolor{g r e e n}{\frac{1}{x + 4} - \textcolor{w h i t e}{.} \frac{2 \textcolor{red}{\left(x + 4\right)}}{\textcolor{red}{x + 4}}}$

$\textcolor{g r e e n}{\frac{1 - 2 x + 8}{x + 4}}$

$\textcolor{g r e e n}{\frac{- 2 x + 9}{x + 4}}$

But $- 2 x + 9 \text{ is the same as } - \left(2 x - 9\right)$ giving

$\textcolor{g r e e n}{\frac{- \left(2 x - 9\right)}{+ \left(x + 4\right)} = - \frac{2 x - 9}{x + 4}}$