A correct solution came from Bradley student Lena Folwaczny.
Other correct solutions were submitted by
Bill Webb, Nancy Schwarzkopf, Aaron Kahn, Juan Carlos Marivela,
A. Teitelman, Al Zimmermann, Ron Welch and Bryan Fluhrer.
Since a / b < c / d, a d < b c.
This means that a (b + d) = a b + a d < a b + b c = b (a + c),
so a / b < (a + c) / (b + d).
It also means that (a + c) d = a d + c d < b c + c d = (b + d) c,
so (a + c) / (b + d) < c / d.