Combustion Secret Formula

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.