resolve into partial fraction x²/(x+1)².(x+2)
Answers
Answer:
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Answer:
x2/(x+1)2.(x+2) = A/x+2 + B/(x+1) + C/(x+1)2 --------------- 1
multiply both sides by (x+1)2 . (x+2), we get
x2 = A(x+1)2 + B(x+1)(x+2) + C(x+2) ----------------- 2
now, let we put x+2 = 0, we get x = -2
put in 2
(-2)^2 = A(-2+1)^2 + 0 + 0
4 = A
similarly, put x+1 = 0, we get x = -1
put in 2
(-1)^2 = 0 + 0 + C(-1+2)
1 = C
now, compare the co-efficients of x2, we get
x2 = Ax2 + Bx2
1 = A + B
1 = 4 + B
B = 3
put values of A,B, and C in 1, we get
x2/(x+1)2.(x+2) = 4/x+2 + 3/(x+1) + 1/(x+1)2 ans.
Step-by-step explanation: