Question

resolve into the partial fractions 3x+2/(x-2)(x+3)^2​

Answer 1

Step-by-step explanation:

Explanation:

We can factor the denominator as

Here the denominator x2 – 3x + 2 is not a linear factor. So if possible we have to factorise it then only we can split up into partial fraction. x2 – 3x + 2 = (x – 1) (x – 2) Multiply both side by (x – 1) (x – 2) 3x + 7 = A(x – 2) + B(x – 1) … (2) Put x = 2 in (2) we get 3(2) + 7 = A(2 – 2) + B(2 – 1) 6 + 7 = 0 + B(1) ∴ B = 13 Put x = 1 in (2) we get 3(1) + 7 = A(1 – 2) + B(1 – 1) 3 + 7 = A (-1) + 0 10 = A(-1) ∴ A = -10 Using A = -10 and B = 13 in (1) we get Note: When the denominator is only two linear factors we can adopt the following method.

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