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Rational functions/Q/Computing example/Exercise
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Compute in
Q
(
X
)
{\displaystyle {}\mathbb {Q} (X)}
the following expressions.
The product
2
X
3
−
5
X
2
+
X
−
1
X
2
−
2
X
+
6
⋅
X
2
+
3
5
X
3
−
4
X
2
−
7
.
{\displaystyle {\frac {2X^{3}-5X^{2}+X-1}{X^{2}-2X+6}}\cdot {\frac {X^{2}+3}{5X^{3}-4X^{2}-7}}.}
The sum
4
X
3
−
X
2
+
6
X
−
2
X
2
−
4
X
−
3
+
X
2
−
3
3
X
2
+
5
.
{\displaystyle {\frac {4X^{3}-X^{2}+6X-2}{X^{2}-4X-3}}+{\frac {X^{2}-3}{3X^{2}+5}}.}
The inverse of
6
X
3
−
9
X
2
+
5
X
−
1
X
4
−
4
X
3
+
3
X
2
−
8
X
−
3
.
{\displaystyle {\frac {6X^{3}-9X^{2}+5X-1}{X^{4}-4X^{3}+3X^{2}-8X-3}}.}
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