Question

If $\frac{5x-3}{x}+\frac{5y-3}{y}+\frac{5z-3}{z}=0$ then find the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$.

Answer 1

Given, $\frac{5x-3}{x}+\frac{5y-3}{y}+\frac{5z-3}{z}=0$

or, $5-\frac{3}{x}+5-\frac{3}{y}+5-\frac{3}{z}=0$

or, $15=3(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})$

or, $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{15}{3}$

or, $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=5.$