Answer:
x=-2
Step-by-step explanation:
[tex] \frac{1}{6{x}^{2} } = \frac{1}{2x} + \frac{7}{6 {x}^{2} } \\ \frac{7}{6 {x}^{2} } - \frac{1}{6{x}^{2} } + \frac{1}{2 {x} } = 0 \: \: \: \: \: ( - \frac{1}{6 {x}^{2} } \: throughout) \\ \frac{6}{6 {x}^{2} } + \frac{1}{2x} = 0 \: \: \: \: \: (simplify)\\ \frac{1}{ {x}^{2} } + \frac{1}{2x} = 0 \\ \frac{2 {x}^{2} }{ {x}^{2} } + \frac{2 {x}^{2} }{2x} = 0 \: \: \: \: \: ( \times 2 {x}^{2} \: throughout) \\ 2 + x = 0 \: \: \: \: \: (simplify)\\ x = - 2[/tex]
