Question 8
Let $a, b, c, d$ be positive integers satisfying
$$
\frac{a b}{a+b}+\frac{c d}{c+d}=\frac{(a+b)(c+d)}{a+b+c+d}
$$
Determine all possible values of $a+b+c+d$.
$$
\frac{a b}{a+b}+\frac{c d}{c+d}=\frac{(a+b)(c+d)}{a+b+c+d}
$$
Determine all possible values of $a+b+c+d$.