If ab+xy-xb=0 and bc+yz-cy=0, then what is \frac{x}{a}+\frac{c}{z} equal to?

Explanation

From the first equation, x(b-y) = ab \Rightarrow \frac{x}{a} = \frac{b}{b-y}. From the second equation, c(b-y) = -yz \Rightarrow \frac{c}{z} = \frac{-y}{b-y}. Adding these results together: \frac{x}{a} + \frac{c}{z} = \frac{b}{b-y} + \frac{-y}{b-y} = \frac{b-y}{b-y} = 1.

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