Solve: \( \frac{1}{3 a^{2}}-\frac{1}{a}=\frac{1}{6 a^{2}} \) The solution is \( a=\square \)

We start with the equation \[ \frac{1}{3 a^2} - \frac{1}{a} = \frac{1}{6 a^2}. \] **Step 1.** Multiply both sides of the equation by \(6a^2\) to eliminate the denominators. Note that \(a \neq 0\). \[ 6a^2 \cdot \left(\frac{1}{3 a^2} - \frac{1}{a}\right) = 6a^2 \cdot \frac{1}{6a^2}. \] **Step 2.** Simplify each term. The first term: \[ 6a^2 \cdot \frac{1}{3a^2} = \frac{6}{3} = 2. \] The second term: \[ 6a^2 \cdot \frac{1}{a} = 6a. \] The right-hand side: \[ 6a^2 \cdot \frac{1}{6a^2} = 1. \] Thus, the equation becomes: \[ 2 - 6a = 1. \] **Step 3.** Solve for \(a\). Subtract 2 from both sides: \[ -6a = 1 - 2, \] \[ -6a = -1. \] Divide by \(-6\): \[ a = \frac{-1}{-6} = \frac{1}{6}. \] The solution is \( a = \frac{1}{6} \).