Answer
$(−\infty,−7)\cup(−7,3)∪(3,\infty)$
Work Step by Step
$f(x) = \frac{x^{2} + 1}{(x^{2} + 4x -21}$
The function is defined for all real numbers except those for which the denominator is zero.
To find the domain of this function, we need to solve the equation $x^{2} + 4x -21 = 0 $ so we can exclude those $x$ values from the real number set.
$ x^{2} + 4x -21 = 0 $
$(x - 3)(x + 7) = 0$
$x = 3$ or $x = - 7 $
Therefore the domain of the function is
$(−\infty,−7)\cup(−7,3)∪(3,\infty)$
