Question

If 3-2x/x + 3-4y/y + 3-5z/z=0 find the value of 1/x + 1/y + 1/z. Please solve fast​. Answer is 11/3 show the process ​​

Answer 1

Given ;

$\frac{3 - 2x}{x} + \frac{3 - 4y}{y} + \frac{3 - 2z}{z} = 0$

To find ;

$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = ?$

Solution ;

$\frac{3 - 2x}{x} + \frac{3 - 4y}{y} + \frac{3 - 5z}{z} = 0 \\ \\ \frac{3}{x} - \frac{2x}{x} + \frac{3}{y} - \frac{4y}{y} + \frac{3}{z} - \frac{5z}{z} = 0 \\ \\ \frac{3}{x} - 2 + \frac{3}{y} - 4 + \frac{3}{z} - 5 = 0 \\ \\ - 2 - 4 - 5 + \frac{3}{x} + \frac{3}{y} + \frac{3}{z} = 0 \\ \\ - 11 + \frac{3}{x} + \frac{3}{y} + \frac{3}{z} = 0 \\ \\ take \: \: 3 \: \: as \: \: common \\ \\ 3( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} ) = 11 \\ \\ \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{11}{3}$

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