$\frac{x^2+3}{(x+5)(x+6)}=1-\frac{11x+27}{(x+5)(x+6)}$
If you substitute $x$ with any ordinary value like $2$, you will find that value of the numerator is lower than the denominator's. So why do we still have to perform long division to get partial fractions when this is clearly not an improper fractions?