First we have to factorise the denominator
It can be factorised as,
Then the fraction can be written as,
This fraction can be resolved into partial fractions by writing it as the sum of a fraction having denominator
and a fraction having denominator
Since
is a first degree polynomial, the numerator of the fraction having this term as denominator should be a zero degree polynomial, or a constant term, assumed as
Since
is a second degree polynomial, the numerator of the fraction having this term as denominator should be a first degree polynomial, assumed as
So let,
Equating numerators,
Equating corresponding coefficients,
Solving these three equations we get,
Thus,
So (1) becomes,
Hence the given fraction is resolved into partial fractions.