Question

if 2x=3y=6-z find the value 1/x+1/y+1/z​

Answer 1

Answer:

$2x = 3y = 6 - z \\ \\ 3y = 2x \\ y = \frac{2x}{3} \\ \\ 3y = 6- z \\ y = \frac{ 6- z}{3} \\ \\ \frac{2x}{3} = \frac{6 - z}{3} \\ 2x =6 - z \\ x = \frac{6 - z}{2} \\ \\ 6 - z = 2x \\ z = 6 - 2x \\ \\ \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \\ = \frac{1}{6 - z} + \frac{1}{ \frac{2x}{3} } + \frac{1}{6 - 2x} \\ = \frac{1}{6 - z} + \frac{3}{2x} + \frac{1}{6 - 2x}$

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