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Solve the following equation: 1/x - 1/x-2 = 3.\(\frac1x - \frac1{x -2} = 3, \,x\ne0,2 \) |
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Answer» \(\frac1x - \frac1{x -2} = 3, \,x\ne0,2 \) ⇒ \(\frac{x -2-x}{x(x -2)}=3\) ⇒ \(-2 = 3x^2 - 6x\) ⇒ \(3x^2 - 6x + 2 = 0\) ⇒ \(x = \frac{6\pm\sqrt{36-24}}{6}\) \(= \frac{6 \pm2\sqrt3}{6}\) \(= \frac{3\pm\sqrt3}{3}\) \(= 1\pm \frac1{\sqrt3}\) Hence, solutions are \( 1+ \frac1{\sqrt3}\) or \( 1- \frac1{\sqrt3}\). |
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