# Combustion Secret Formula

**Chemistry**Level pending

The compound \(C_aH_bO_c\) reacts completely with oxygen gas to produce carbon dioxide and water. For every mole of \(C_aH_bO_c\) reacted, \(xa+yb-zc\) moles of oxygen are also combusted.

If \(x+y+z\) can be written in the form \(\frac{M}{N},\) where \(M\) and \(N\) are positive coprime integers, find \(M+N.\)

You may assume that the compound \(C_aH_bO_c\) exists, and that \(a\) and \(b\) are positive integers while \(c\) is a non-negative integer.