x = -4 is not undefined because f(x) = x+4 is in the top part, the numerator, not the denominator. So the value that makes f(x) = x + 4 zero does not result in a division by zero.
Indeed, if we try to evaluate (f/g)(-4), then we get
[tex]\displaystyle\left( \frac{f}{g}\right)(-4) = \frac{f(-4)}{g(-4)} = \frac{-4+4}{-4-3} = \frac{0}{-7} = 0,[/tex]
which does not involve a division by zero.
However, attempting to evaluate (f/g)(3) leads us to
[tex]\displaystyle\left( \frac{f}{g}\right)(3) =\frac{3+4}{3-3} = \frac{7}{0},[/tex]
which involves a division by zero, and divisions by zero are undefined
