Question

resolve into partial fraction 9 ÷ (x-1)(x+2)²

Answer 1

Resolve
Solution:
7x  25 into partial fractions. (x  3)(x  4)
7x  25 = A  B ------------------(1) (x3)(x4) x3 x4
Multiplying both sides by L.C.M. i.e., (x – 3)(x – 4), we get 7x – 25 = A(x – 4) + B(x – 3) -------------- (2)
7x – 25 = Ax – 4A + Bx – 3B
Chapter 4 86 Partial Fraction
have
7x – 25 = Ax + Bx – 4A – 3B
7x – 25 = (A + B)x – 4A – 3B
Comparing the co-efficients of like powers of x on both sides, we
7 = A + B and
–25 = – 4A – 3B Solving these equation we get
A = 4 and B = 3
Hence the required partial fractions are:
7x25 43 (x3)(x4) x3 x4
Alternative Method:
Since 7x – 25 = A(x – 4) + B(x – 3) Put x -4 = 0,  x = 4 in equation (2)
7(4) – 25 = A(4 – 4) + B(4 – 3) 28 – 25 = 0 + B(1)
B=3
Put x – 3 = 0  x = 3 in equation (2) 7(3) – 25 = A(3 – 4) + B(3 – 3)
21 – 25 = A(–1) + 0
– 4 =– A
A =4
Hence the required partial fractions are
7x25 43
(x3)(x4) x3 x4
Note : The R.H.S of equation (1) is the identity equation of L.H.S


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Answer 2

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