I
X
Resolve
into Partial Fractions.
x⁴/x²-3x+2
Answers
Answered by
0
Answer:
ANSWER
The first thing is to factor the denominator and get the form of the partial fraction decomposition
⇒
(x
2
+1)(x+5)
26x
2
+208x
=
x
2
+1
Ax+B
+
x+5
C
The next step is to set numerators equal
⇒26x
2
+208x=(Ax+B)(x+5)+C(x
2
+1)
⇒26x
2
+208x=(A+C)x
2
−x(5A+B)+(5B+C)
we can just pick a few values of x and find the constants so let’s do that
⇒ x=0 5B+C=0.....................(1)
⇒ x=1 2C+6A+6B=234...........(2)
⇒ x=−1 2C−4A+4B=−182......(3)
Now, by solving eq 1,2,3, we get
A=41, B=3, C=−15
⇒
(x
2
+1)(x+5)
26x
2
+208
=
x
2
+1
41x+3
−
x+5
15
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