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