Ta có: \(\frac{a}{x}+\frac{y}{b}=1\)
\(\rightarrow\frac{a}{x}\cdot\frac{b}{y}+\frac{y}{b}\cdot\frac{b}{y}=1\cdot\frac{b}{y}\)
\(\rightarrow\frac{ab}{xy}+1=\frac{b}{y}\left(1\right)\)
Ta có: \(\frac{b}{y}+\frac{z}{c}=1\)
\(\rightarrow\frac{b}{y}=1-\frac{z}{c}\left(2\right)\)
Từ (1) và (2) \(\rightarrow\frac{ab}{xy}+1=1-\frac{z}{c}\)
\(\rightarrow\frac{ab}{xy}=\frac{-z}{c}\) \(\rightarrow abc=-xyz\)
\(\rightarrow abc+xyz=0\)