Answer
Incorrect.
On the RHS,
$\displaystyle \frac{B}{x^{2}+4}$ should be replaced wirh $\displaystyle \frac{Bx+C}{x^{2}+4}$
Work Step by Step
On the RHS, the term $\displaystyle \frac{A}{x+1}$ is correct,
(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. )
But, the term $\displaystyle \frac{B}{x^{2}+4}$ is incorrect.
(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. )
$\displaystyle \frac{B}{x^{2}+4}$ should be replaced wirh $\displaystyle \frac{Bx+C}{x^{2}+4}$
