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

To solve the equation \( \frac{1}{3 a^{2}} - \frac{1}{a} = \frac{1}{6 a^{2}} \), we will first find a common denominator. The common denominator for the left side can be \( 6a^{2} \). Rewriting the left side: \[ \frac{2}{6a^{2}} - \frac{6}{6a^{2}} = \frac{2 - 6}{6a^{2}} = \frac{-4}{6a^{2}} = \frac{-2}{3a^{2}} \] Setting this equal to the right side gives: \[ \frac{-2}{3a^{2}} = \frac{1}{6a^{2}} \] Now, cross-multiply: \[ -2 \cdot 6 = 1 \cdot 3 \Rightarrow -12 = 3 \] This is not possible, which means we must have made an arithmetic oversight. Let's go back to the original setup. On simplifying the fractions correctly again: From: \[ \frac{1}{3a^2} - \frac{1}{a} - \frac{1}{6a^2} = 0 \] Combine the fractions: \[ \frac{2}{6a^{2}} - \frac{6}{6a^{2}} - \frac{1}{6a^2} = 0 \] Thus: \[ \frac{2 - 6 - 1}{6a^{2}} = \frac{-5}{6a^2} = 0 \] Set the numerator to zero (the fraction can’t equal zero if the denominator is non-zero): \(-5 = 0\) again indicates why there is no solution under standard rules. Therefore, the solution doesn't lend itself to real numbers but rather points to the oversight rather than a value. Thus, there are no valid solutions in real numbers. The solution is \( a=\) no solution.