(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.<br /><br />The quadratic expression \(m^2 + 15m + 56\) can be factored as follows:<br />We look for two numbers that multiply to 56 and add up to 15. These numbers are 7 and 8.<br />So, \(m^2 + 15m + 56 = (m + 7)(m + 8)\).<br /><br />Now, we rewrite the original expression with the factored form:<br />\[<br />\frac{3}{(m + 7)(m + 8)} + \frac{4}{m + 8}<br />\]<br /><br />Next, we find a common denominator for the two fractions. The common denominator is \((m + 7)(m + 8)\).<br /><br />We rewrite each fraction with the common denominator:<br />\[<br />\frac{3}{(m + 7)(m + 8)} + \frac{4(m + 7)}{(m + 7)(m + 8)}<br />\]<br /><br />Now, we combine the fractions:<br />\[<br />\frac{3 + 4(m + 7)}{(m + 7)(m + 8)}<br />\]<br /><br />Simplify the numerator:<br />\[<br />3 + 4(m + 7) = 3 + 4m + 28 = 4m + 31<br />\]<br /><br />So, the simplified expression is:<br />\[<br />\frac{4m + 31}{(m + 7)(m8)}<br />\]<br /><br />Thus, the simplified form of the given expression is:<br />\[<br />\boxed{\frac{4m + 31}{(m + 7)(m + 8)}}<br />\]