Question

Resolve into partial fraction for the following:

`(3x + 7)/(x^2 - 3x + 2)`

Answer 1

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)

`(3x + 7)/((x - 1)(x - 2)) = "A"/(x - 1) + "B"/(x - 2)`   ...(1)

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

`(3x + 7)/((x - 1)(x - 2)) = (-10)/(x - 1) + 13/(x - 2)`

`= 13/(x - 2) + (-10)/(x - 1)`

Thus `(3x + 7)/((x - 1)(x - 2)) = 13/(x - 2) + (-10)/(x - 1)`