## College Algebra (6th Edition)

$\displaystyle \frac{5x^{2}-6x+7}{(x-1)(x^{2}+1)}=\frac{A}{x-1}+\frac{Bx+C}{x^{2}+1}$
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: $\displaystyle \frac{5x^{2}-6x+7}{(x-1)(x^{2}+1)}=\frac{A}{x-1}+\frac{Bx+C}{x^{2}+1}$