resolve into partial fractions 3x² - 8x²+10 / (x-1)
Answers
Step-by-step explanation:
(x−1)
4
3x
3
−8x
2
+10
can be resolved into partial fraction as
x−1
A
+
(x−1)
2
B
+
(x−1)
3
C
+
(x−1)
4
D
So , 3x
3
−8x
2
+10=A(x−1)
3
+B(x−1)
2
+C(x−1)+D
Put x=1 , we get 3−8+10=D
D=5
Comparing the coefficient of x
3
on both sides we get , A=3 .
So equation reduces to 3x
3
−8x
2
+10=3(x−1)
3
+B(x−1)
2
+C(x−1)+5
Now compare the constant on both sides , 10=−3+B−C+5
=>8=B−C - (1)
Comparing the coefficent of x
2
we get −8=−9+B
=>B=1
So , put B=1 in (1) , we get C=−7
Therefore ,
(x−1)
4
3x
3
−8x
2
+10
=
x−1
3
+
(x−1)
2
1
−
(x−1)
3
7
+
(x−1)
4
5