The function h(x) is undefined when the denominator of
1
(x−5)2+4(x−5)+4
is equal to zero. The expression(x−5)2+4(x−5)+4 is a perfect square:
(x−5)2+4(x−5)+4=((x−5)+2)2
which can be rewritten as (x−3)2 The expression (x−3)2 is equal to zero if and only if x=3. Therefore, the value of x for which h(x) is undefined is 3.