Answer
$\displaystyle \frac{5x^{2}-9\mathrm{x}+19}{(x-4)(x^{2}+5)}=\frac{\mathrm{A}}{x-4}+\frac{\mathrm{B}\mathrm{x}+\mathrm{C}}{x^{2}+5}$
Work Step by Step
For the factor $(x-4),$
see p.541. Decomposition with Distinct Linear Factors In the Denominator:
Include one partial fraction with a $constant$ numerator
for each distinct linear factor in the denominator.
On the RHS, the corresponding term will be $\displaystyle \frac{A}{x-4}$
For the factor $(x^{2}+\mathit{5})$
see p.545. Nonrepeated Prime Quadratic Factors In the Denominator
Include one partial fraction with a $linear$ numerator
for each distinct prime quadratic factor in the denominator.
On the RHS, the corresponding term will be $\displaystyle \frac{Bx+C}{x^{2}+5}$
Setup only:
$\displaystyle \frac{5x^{2}-9\mathrm{x}+19}{(x-4)(x^{2}+5)}=\frac{\mathrm{A}}{x-4}+\frac{\mathrm{B}\mathrm{x}+\mathrm{C}}{x^{2}+5}$
