Given the function:
[tex]g(x)=\frac{x+1}{(x+1)(x-1)}[/tex]Let's find the domain of the function.
The domain is all set of x values which makes the function defined.
To find the domain, set the denominator to zero and solve for x.
We have:
(x + 1)(x - 1) = 0
Set the individual factors to zero and solve for x.
x + 1 = 0
Subtract 1 from both sides:
x + 1 - 1 = 0 - 1
x = -1
x - 1 = 0
Add 1 to both sides:
x - 1 + 1 = 0 + 1
x = 1
Therefore, the domain of the function in interval notation is:
[tex]\mleft(-\infty,-1\mright)\cup(-1,1)\cup(1,\infty)[/tex]ANSWER:
[tex]\mleft(-\infty,-1\mright)\cup(-1,1)\cup(1,\infty)[/tex]
