Step-by-step explanation:
First, factor the numerator and denominator.
⎧
⎪
⎨
⎪
⎩
k
(
x
)
=
5
+
2
x
2
2
−
x
−
x
2
=
5
+
2
x
2
(
2
+
x
)
(
1
−
x
)
To find the vertical asymptotes, we determine where this function will be undefined by setting the denominator equal to zero:
{
(
2
+
x
)
(
1
−
x
)
=
0
x
=
−
2
,
1
Neither
x
=
−
2
