Answer
$$\eqalign{
& {\text{It is needed apply the long division}} \cr
& {\text{before applying the method of partial fractions}} \cr} $$
Work Step by Step
$$\eqalign{
& {\text{There are no constants }}A{\text{ and }}B{\text{ that satisfying }}\frac{{{x^2}}}{{\left( {x - 4} \right)\left( {x + 5} \right)}} = \frac{A}{{x - 4}} + \frac{B}{{x + 5}},{\text{ because the}} \cr
& \frac{{{x^2}}}{{\left( {x - 4} \right)\left( {x + 5} \right)}}{\text{ is a improper fraction }}\frac{{{x^2}}}{{{x^2} + x - 20}},{\text{ so it is needed apply the long division}} \cr
& {\text{before applying the method of partial fractions}}{\text{.}} \cr} $$
