Identifying Holes in Rational Functions
Given the rational function
f
(
x
)
=
\displaystyle \ {f{{\left({x}\right)}}}=
f
(
x
)
=
x
2
+
13
x
+
36
x
2
−
16
x
+
63
\displaystyle \frac{{{x}^{{2}}+{13}{x}+{36}}}{{{x}^{{2}}-{16}{x}+{63}}}
x
2
−
16
x
+
63
x
2
+
13
x
+
36
\displaystyle \ \
find any hole(s) of the function.
x
=
9
\displaystyle {x}={9}
x
=
9
x
=
−
9
,
x
=
−
4
\displaystyle {x}=-{9},\ {x}=-{4}
x
=
−
9
,
x
=
−
4
x
=
−
4
\displaystyle {x}=-{4}
x
=
−
4
x
=
7
\displaystyle {x}={7}
x
=
7
x
=
9
,
x
=
7
\displaystyle {x}={9},\ {x}={7}
x
=
9
,
x
=
7
There are no holes
-9,-4,9,7
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