If x(3 - frac{2}{x}) = frac{3}{x}, x neq 0, t | vedclass

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(C) Given equation: $x(3 - \frac{2}{x}) = \frac{3}{x}$Expanding the left side: $3x - 2 = \frac{3}{x}$Rearranging the terms: $3x - \frac{3}{x} = 2$Divi

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$2 \frac{4}{9}$

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(C) Given equation: $x(3 - \frac{2}{x}) = \frac{3}{x}$Expanding the left side: $3x - 2 = \frac{3}{x}$Rearranging the terms: $3x - \frac{3}{x} = 2$Dividing both sides by $3$: $x - \frac{1}{x} = \frac{2}{3}$Squaring both sides: $(x - \frac{1}{x})^2 = (\frac{2}{3})^2$$x^2 + \frac{1}{x^2} - 2 = \frac{4}{9}$Adding $2$ to both sides: $x^2 + \frac{1}{x^2} = \frac{4}{9} + 2$$x^2 + \frac{1}{x^2} = \frac{4 + 18}{9} = \frac{22}{9}$Converting to mixed fraction: $\frac{22}{9} = 2 \frac{4}{9}$

If $x(3 - \frac{2}{x}) = \frac{3}{x}, x \neq 0,$ then the value of $x^2 + \frac{1}{x^2}$ is

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