Resolving into partial fractions 3x-1/(x-2)(x-3)
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Answered by
1
Answer:
Let
(x
2
+x+1)(x+1)
2
x
3
−3x−2
=
x
2
+x+1
Ax+B
+
x+1
C
+
(x+1)
2
D
⇒x
3
−3x−2=(Ax+B)(x+1)
2
+C(x
2
+x+1)(x+1)+D(x
2
+x+1)
⇒x
3
−3x−2=A(x
3
+2x
2
+2x)+B(x
2
+2x+1)+C(x
3
+2x
2
+2x+1)+D(x
2
+x+1)
On comapring coefficients we get
A+C=1,2A+B+2C+D=0,2A+2B+2C+D=−3,B+C+D=−2
⇒A=3,B=−1,C=−3,D=2
Hence
(x
2
+x+1)(x+1)
2
x
3
−3x−2
=
x
2
+x+1
3x−1
+
x+1
−3
+
(x+1)
2
2
Hence, option 'A' is correct.
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