Question : What is the value of $\left(\frac{1}{a} - \frac{1}{b} - \frac{1}{c}\right)$, if $\frac{2a - 5}{a} - \frac{4b - 5}{b} + \frac{6c + 5}{c} = 0$?
Option 1: $\frac{4}{5}$
Option 2: $-\frac{8}{5}$
Option 3: $\frac{2}{5}$
Option 4: $-\frac{12}{5}$
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Correct Answer: $\frac{4}{5}$
Solution :
$\frac{2a- 5}{a} - \frac{4b - 5}{b} + \frac{6c + 5}{c} = 0$
$⇒(2 -\frac{5}{a}) - (4 - \frac{5}{b}) + (6 + \frac{5}{c})=0$
$⇒ -\frac{5}{a} + \frac{5}{b} + \frac{5}{c} = -4$
$⇒–(\frac{1}{a}- \frac{1}{b} - \frac{1}{c}) =-\frac{4}{5}$
$\therefore(\frac{1}{a} - \frac{1}{b} - \frac{1}{c}) = \frac{4}{5}$
Hence, the correct answer is $\frac{4}{5}$.
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