Answer
$\displaystyle \frac{5x^{2}-6x+7}{(x-1)(x^{2}+1)}=\frac{A}{x-1}+\frac{Bx+C}{x^{2}+1}$
Work Step by Step
For the factor $(x-1),$
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 $\displaystyle \frac{A}{x-1}$
For the factor $(x^{2}+1)$
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 $\displaystyle \frac{Bx+C}{x^{2}+1}$
Setup only:
$\displaystyle \frac{5x^{2}-6x+7}{(x-1)(x^{2}+1)}=\frac{A}{x-1}+\frac{Bx+C}{x^{2}+1}$
