Question

Factorise.
${6x }^{2} - \frac{2}{x} = 1$
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Answer 1

${6x }^{2} - \frac{2}{x} = 1 \\ \\ {6x }^{2} - \frac{2}{x} - 1 = 0 \\ \\ \frac{ {6x}^{3} - 2 - x}{x} = 0 \\ \\ {6x}^{3} - 2 - x = x \\ \\ {6x}^{3} - 2 - x - x = 0 \\ {6x}^{3} - 2 - 2x = 0 \\ 2x( {3x}^{2} - 1) - 2 = 0 \\ 2x( {3x}^{2} - 1) = 2 \\ {3x}^{2} - 1 = \frac{2}{2x} \\ {3x}^{2} = \frac{2}{2x} + 1 \\ \\ {3x}^{2} = \frac{2 + 2x}{2x} \\ \\ {x}^{2} = \frac{2 + 2x}{2x \times 3} \\ \\ {x}^{2} = \frac{2(x + 1)}{6x} \\ \\ {x}^{2} = \frac{x + 1}{3x} \\ \\ x = \sqrt{ \frac{x + 1}{3x} }$






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