Question

Solve the following equation:
1/x - 1/(x-2) = 3 , while x ≠ 0, 2

Answer 1

$\frac{1}{x} - \frac{1}{(x - 2)} = 3 \\ \\ cross \: multiply \\ \\ \frac{(x - 2) - x}{ {x}^{2} - 2x } = 3 \\ \\ - 2 = 3 {x}^{2} - 6x \\ \\ 3 {x}^{2} - 6x + 2 = 0 \\ \\ x = \frac{6 ( + or - ) \sqrt{ {6}^{2} - (4 \times 3 \times 2)} }{(2 \times 3)} \\ \\ x = \frac{6( + or - ) \sqrt{12} }{6} \\ \\ x = \frac{3( + or - ) \sqrt{3} }{3} \\ \\ x = \frac{3 + \sqrt{3} }{3} \: or \: \frac{3 - \sqrt{3} }{3}$