Answer
$\frac{3m+4}{m-7}$
$m \ne\ 7$ and $m \ne -4$
Work Step by Step
To simplify the expression, we need to arrange the numerator and denominator in descending powers and then factor the numerator and denominator.
$\frac{16 + 16m +3m^2}{m^2 - 3m - 28}$ = $\frac{3m^2+16m+16}{m^2 - 3m - 28}$ = $\frac{$(3m+4)(m+4}{(m-7)(m+4)}$
Now we can divide out the common factor of $(m+4)$
$\frac{(3m+4)(m+4}{(m-7)(m+4)}$ = $\frac{3m+4}{m-7}$
To find the excluded values, we need to look at the factored expression before simplifying:
$\frac{$(3m+4)(m+4}{(m-7)(m+4)}$
Setting each factor of the denominator equal to 0, we will find the excluded values:
$m-7 = 0$
$m=7$
$m+4 = 0$
$m = -4$
Therefore, $m \ne\ 7$ and $m \ne -4$
