Solve the expression (2x2 + 7x + 33) / (x3 + x2 - 1/x) into partial fractions.

Step 1: Factor the denominator.
Find two numbers that multiply to $12$ and add to $7$: $3$ and $4$.
$n^{2} + 7n + 12 = (n + 3)(n + 4)$

Step 2: Set up the partial fraction decomposition.
$\frac{27}{(n + 3)(n + 4)} = \frac{a}{n + 3} + \frac{b}{n + 4}$

Step 3: Multiply both sides by $(n + 3)(n + 4)$.
$27 = a(n + 4) + b(n + 3)$

Step 4: Solve for $a$. Substitute $n = -3$.
$27 = a(-3 + 4) + b(-3 + 3)$
$27 = a(1) + b(0)$
$a = 27$

Step 5: Solve for $b$. Substitute $n = -4$.
$27 = a(-4 + 4) + b(-4 + 3)$
$27 = a(0) + b(-1)$
$b = -27$

Step 6: Write the decomposition.
$\frac{27}{n + 3} + \frac{-27}{n + 4} = \frac{27}{n + 3} - \frac{27}{n + 4}$

Final answer:
\dfrac{27{n+3} - \dfrac{27}{n+4}}