Question

$\frac{1}{x } - \frac{1}{x - 2} = 3$

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Answer 1

Answer:

$\frac{1}{x} - \frac{1}{x - 2} = 3 \\ take \: lcm \: \\ lcm \: (x \: and \: x - 2) = x(x - 2) \\ then \\ \frac{(x - 2) - x}{x(x - 2)} = 3 \\ by \: cross \: multiplication \\ x - 2 - x = 3x(x - 2) \\ - 2 = 3 {x}^{2} - 6x \\ 3 {x}^{2} - 6x + 2 = 0 \\ so \: x = \frac{ - (- 6 )\frac{ + }{} \sqrt{ {( - 6)}^{2} - 4(3)(2)} }{2 \times 3} \\ = \frac{6 \frac{ + }{} \sqrt{36 - 24} }{6} \\ = 1 \frac{ + }{} \frac{ \sqrt{12} }{6} \\ so \: x = 1 + \frac{ \sqrt{12} }{6} \\ or \: 1 - \frac{ \sqrt{12} }{6}$