$$\fracP(x)x^2+5x+6 = \frac6x-1x+3$$
$$P(x) \cdot (x+3) = (x^2+5x+6) \cdot (6x-1)$$
$$P(x) = \frac(x^2+5x+6) \cdot (6x-1)(x+3)$$
Observe que $x^2+5x+6=(x+2) \cdot (x+3)$
$$P(x) = \frac(x+2) \cdot (x+3) \cdot (6x-1)(x+3)$$
$$P(x) = \frac(x+2) \cdot \cancel(x+3) \cdot (…)