Question

If (5x-3)/x + (5y-3)/y + (5z-3)/z = 0, then the value of 1/x + 1/y + 1/z is

Answer 1

,Hey friend,here is your answer

Answer 2

$Given \:\frac{(5x-3)}{x} + \frac{(5y-3)}{y} + \frac{(5z-3)}{z} = 0$

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

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

$\implies 15 - \frac{3}{x} - \frac{3}{y} - \frac{3}{z} = 0$

$\implies 15 - \Big(\frac{3}{x} +\frac{3}{y} + \frac{3}{z}\Big ) = 0$

$\implies 15 = \Big(\frac{3}{x} +\frac{3}{y} + \frac{3}{z}\Big )$

$\implies 15 = 3\Big(\frac{1}{x} +\frac{1}{y} + \frac{1}{z}\Big )$

$\implies \frac{15}{3} = \Big(\frac{1}{x} +\frac{1}{y} + \frac{1}{z}\Big )$

$\implies 5 = \Big(\frac{1}{x} +\frac{1}{y} + \frac{1}{z}\Big )$

Therefore.,

$\red{ \Big(\frac{1}{x} +\frac{1}{y} + \frac{1}{z}\Big ) }\green { = 5 }$

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