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Mathematics
Problem
For the rational function
h
(
x
)
=
x
2
+
3
x
(
x
2
−
2
(
k
−
1
)
x
+
k
2
+
1
)
,
h(x)=\frac{x^2+3}{x\bigl(x^2-2(k-1)x+k^2+1\bigr)},
h
(
x
)
=
x
(
x
2
−
2
(
k
−
1
)
x
+
k
2
+
1
)
x
2
+
3
,
find all real values of
k
k
k
such that
x
=
0
x=0
x
=
0
is the only real number at which
h
(
x
)
h(x)
h
(
x
)
is undefined.
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