Resolve into partial fraction : ³+
²−4
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0
Answer:
3x
3
−8x
2
+10
Let x−1=y
Then, x=y+1
(x−1)
4
3x
3
−8x
2
+10
=
y
4
3(y+1)
3
−8(y+1)
2
+10
=
y
4
3(y
3
+1+9y
2
+9y)−8(y
2
+2y+1)+10
=
y
4
3y
3
+3+27y
2
+27y−8y
2
−16y−8+10
=
y
4
3y
3
+19y
2
+11y+5
=
y
3
+
y
2
19
+
y
3
11
+
y
4
5
=
(x−1)
3
+
(x−1)
2
19
+
(x−1)
3
11
+
(x−1)
4
5
∴ The required partial fraction is
(x−1)
4
3x
3
−8x
2
+10
=
(x−1)
3
+
(x−1)
2
19
+
(x−1)
3
11
+
(x−1)
4
5
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