解:因为$\frac {a}{a + b} = k,$所以$a = k(a + b);$
同理$\frac {c}{c + d} = k$得$c = k(c + d),$$\frac {e}{e + f} = k$得$e = k(e + f)。$
则$a + c + e = k(a + b) + k(c + d) + k(e + f) $
$= k[(a + b) + (c + d) + (e + f)]。$
因此$\frac {a + c + e}{a + b + c + d + e + f} = \frac {k[(a + b) + (c + d) + (e + f)]}{(a + b) + (c + d) + (e + f)} = k。$