Question 85127
Since we cannot divide by zero, we can find exclusions in the domain by setting the denominator equal to zero and solving for x:


{{{x+5=0}}} Set the denominator equal to zero

{{{x=-5}}} Solve for x


Since x=-5 makes the denominator equal to zero, we must exclude -5 from our domain. So our domain is: x is the set of all real numbers, except x cannot equal -5. Basically we can choose any number we want, except -5, and plug it in for x to get a real number output.

 

In interval notation, the domain would look like this:



*[Tex  \LARGE (-\infty, -5 )\cup (-5,\infty)] where the "U" stands for union 


Notice when we graph the equation {{{y=(6x+5)/(x+5)}}} we get


{{{ graph( 300, 200, -10, 10, -10, 10, (6x+5)/(x+5)) }}}


and you can see that x=-5 is not part of the domain (note: the vertical line is not part of the graph, it is an asymptote)