Answer
$1$
Work Step by Step
Step by step multiplication of rational expressions:
1. Factor completely what you can
2. Reduce (divide) numerators and denominators by common factors.
3. Multiply the remaining factors in the numerators and
multiply the remaining factors in the denominators. $(\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS})$
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Factor what we can:
$x^{2}+9x+14=...$
... factor the trinomial $x^{2}+bx+c$
... by searching for two factors of $c$ whose sum is $b$.
... Here, we find that $7$ and $2 $are factors of $14$ whose sum is $9.$
$=(x+2)(x+7)$
The problem becomes
$...=\displaystyle \frac{(x+2)(x+7)\cdot 1}{(x+7)\cdot(x+2)}\qquad $... divide out the common factors
$=\displaystyle \frac{1}{1}$
= $1$
