Answer
$\frac{3p + 2}{p + 9}$
Work Step by Step
Factor the numerator by splitting the middle term:
$6p^2 + 21p + 4p + 14$
Group the first two terms and the last two terms:
$(6p^2 + 21p) + (4p + 14)$
Factor out common terms within the groups:
$3p(2p + 7) + 2(2p + 7)$
Group the factors together:
$(3p + 2)(2p + 7)$
Now, we can factor the denominator by splitting the middle term:
$2p^2 + 18p + 7p + 63$
Group the first two terms and the last two terms:
$(2p^2 + 18p) + (7p + 63)$
Factor out common terms within the groups:
$2p(p + 9) + 7(p + 9)$
Group the factors together:
$(2p + 7)(p + 9)$
Put the factored expressions into a fraction:
$\frac{(3p + 2)(2p + 7)}{(2p + 7)(p + 9)}$
Cancel out common factors in the numerator and denominator:
$\frac{3p + 2}{p + 9}$
