How do I factor each of these?

\[ \begin{eqnarray} ab+cd&=&38 \\ ac+bd&=&34\\ ad+bc&=&43\\ \end{eqnarray} \]

Let \(a,b,c\) and \(d\) positive integers such that they satisfy the system of equations above. Find \(a+b+c+d\).

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