Answer
$\frac{(x+5)(x+4)^2}{(x+8)^2(x+7)}$
Work Step by Step
In factored form, the given is equivalent to
$$
\frac{(x+5)(x+4)}{(x+8)(x-3)}\div\frac{(x+8)(x+7)}{(x+4)(x-3)}
.$$
Multiplying by the reciprocal of the divisor, the expression above is equivalent to
$$
\frac{(x+5)(x+4)}{(x+8)(x-3)}\cdot\frac{(x+4)(x-3)}{(x+8)(x+7)}
.$$
Cancelling factors that are common to both the numerator and the denominator, the expression above is equivalent to
$$\begin{aligned}
&
\frac{(x+5)(x+4)}{(x+8)\color{red}{(x-3)}}\cdot\frac{(x+4)\color{red}{(x-3)}}{(x+8)(x+7)}
\\&=
\frac{(x+5)(x+4)(x+4)}{(x+8)(x+8)(x+7)}
\\&=
\frac{(x+5)(x+4)^2}{(x+8)^2(x+7)}
.\end{aligned}$$Hence, the given expression simplifies to $\frac{(x+5)(x+4)^2}{(x+8)^2(x+7)}$.
