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If \(\frac{{11 - 13x}}{x} + \frac{{11 - 13y}}{y} + \frac{{11 - 13z}}{z} = 5\), then what is the value of \(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\)?

If \(\frac{{11 - 13x}}{x} + \frac{{11 - 13y}}{y} + \frac{{11 - 13z}}{z} = 5\), then what is the value of \(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\)? Correct Answer 4

After simplifying the given equation

⇒ 11/x – 13x/x + 11/y – 13y/y + 11/z – 13z/z = 5

⇒ 11/x – 13 + 11/y – 13 + 11/z – 13 = 5

⇒ 11/x + 11/y + 11/z – 39 = 5

⇒ 11(1/x + 1/y + 1/z) = 44

⇒ (1/x + 1/y + 1/z) = 44/11 = 4

∴ 1/x + 1/y + 1/z = 4

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