Answer
$\displaystyle \frac{y+3}{x+3}$
Work Step by Step
1. Factor the numerator and the denominator completely.
2. Divide both the numerator and the denominator by any common factors.
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Numerator $:$ factor in pairs
$xy+2y+3x+6=y(x+2)+3(x+2)=(y+3)(x+2)$
Denominator:
search for integer factors of $6$ whose sum is $5$...
... these are $2$ and $3...$
$ x^{2}+5x+6=(x+2)(x+3)$
Expression = $\displaystyle \frac{(y+3)(x+2)}{(x+2)(x+3)}$
... divide both with the common factor: $(x+2)$
Expression = $\displaystyle \frac{y+3}{x+3}$
