Resolve
4x- 7x² + 5x - 4/
(x²-1)(x² – 3x+2)
into partial fractions
Answers
Answered by
0
Answer:
Correct option is
C
x
2
+1
x
+
x−2
2
+
x−1
1
Let
(x
2
+1)(x
2
−3x+2)
4x
3
−7x
2
+5x−4
=
x
2
+1
Ax+B
+
x−2
C
+
x−1
D
⇒4x
3
−7x
2
+5x−4=(Ax+B)(x−2)(x−1)+C(x
2
+1)(x−1)+D(x
2
+1)(x−2)
⇒4x
3
−7x
2
+5x−4=A(x
3
−3x
2
+2x)+B(x
2
−3x+2)+C(x
3
−x
2
−x−1)+D(x
3
−2x
2
+x−2)
On comparing coefficients we get
A+C+D=4,−3A+B−C−2D=−7,2A−3B−C+D=5,2B−C−2D=−4
⇒A=1,B=0,C=2,D=1
Hence
(x
2
+1)(x
2
−3x+2)
4x
3
−7x
2
+5x−4
=
x
2
+1
x
+
x−2
2
+
x−1
1
Hence, option 'C' is correct.
Was this answer helpful?
Similar questions