Answer:
Step-by-step explanation:
Factor the given function:
(x + 2)(x + 5)
f(x) = --------------------
(x + 5)(x + 4)
The factor (x + 5) can be crossed out in numerator and denominator. There is a 'hole' at x = -5 (which comes from setting (x + 5) = 0 and solving for x).
If we do cancel the (x + 5) factors, we are left with
(x + 2)
f(x) = ------------- . We can't just substitute x = -5 because the original
(x + 4) function is not defined for that x value. However, we
can locate the hole by letting x have the value of a litle more than -5, obtaining:
( -5+ + 2)
f(-5+) = -------------, which comes out to approx. -3/-1, or +3 .
(-5+ + 4)
So the hole location is (-5, 3).
f(x) = --------------------
(x + 5)(x + 4)
