[tex] \frac{-1}{x} +\frac{x}{3} =\frac{1}{6} \\\\(6x)(\frac{-1}{x} +\frac{x}{3}) =(\frac{1}{6} ) (6x)\\\\\frac{-6x}{x} +\frac{6x^{2}}{3} =\frac{6x}{6} \\\\-6+2x^{2} =x\\\\
2x^{2} -x-6=0 \\\\2x^{2} -4x +3x-6=0\\\\2x(x-2)+3(x-2)=0\\\\(2x+3)(x-2)=0\\\\
x=\frac{-3}{2} \; and\;x=2 [/tex]
He factored the quadratic equation incorrectly.
