# What are the excluded values for y=(x+1)/(x-3)?

Mar 29, 2017

Excluded values: $x = 3$ and $y = 1$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} y = \frac{x + 1}{x - 3}$
since division by zero is undefined, we must exclude
$\textcolor{w h i t e}{\text{XXX}} x = 3$

Re-writing the given equation:
$\textcolor{w h i t e}{\text{XXX}} y x - 3 y = x + 1$

$\textcolor{w h i t e}{\text{XXX}} y x - x = 3 y + 1$

$\textcolor{w h i t e}{\text{XXX}} x \left(y - 1\right) = 3 y + 1$

$\textcolor{w h i t e}{\text{XXX}} x = \frac{3 y + 1}{y - 1}$

and (again) since division by zero is undefined, we must exclude:
$\textcolor{w h i t e}{\text{XXX}} y = 1$

This can also be seen graphically by plotting the given equation: