(3)/(m^2)+15m+56+(4)/(m+8)

To simplify the expression $\frac{3}{m^2 + 15m + 56} + \frac{4}{m + 8}$, we first need to factor the quadratic expression in the denominator of the first fraction.

The quadratic expression $m^2 + 15m + 56$ can be factored as follows:
We look for two numbers that multiply to 56 and add up to 15. These numbers are 7 and 8.
So, $m^2 + 15m + 56 = (m + 7)(m + 8)$.

Now, we rewrite the original expression with the factored form:
$$\frac{3}{(m + 7)(m + 8)} + \frac{4}{m + 8}$$

Next, we find a common denominator for the two fractions. The common denominator is $(m + 7)(m + 8)$.

We rewrite each fraction with the common denominator:
$$\frac{3}{(m + 7)(m + 8)} + \frac{4(m + 7)}{(m + 7)(m + 8)}$$

Now, we combine the fractions:
$$\frac{3 + 4(m + 7)}{(m + 7)(m + 8)}$$

Simplify the numerator:
$$3 + 4(m + 7) = 3 + 4m + 28 = 4m + 31$$

So, the simplified expression is:
$$\frac{4m + 31}{(m + 7)(m8)}$$

Thus, the simplified form of the given expression is:
$$\boxed{\frac{4m + 31}{(m + 7)(m + 8)}}$$