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

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{1}{3 a^{2}} - \frac{1}{a} = \frac{1}{6 a^{2}}
$$

**Step 1: Eliminate the Denominators**

Multiply both sides of the equation by the least common multiple of the denominators, which is $$6a^{2}$$:

$$
6a^{2} \left( \frac{1}{3 a^{2}} - \frac{1}{a} \right) = 6a^{2} \left( \frac{1}{6 a^{2}} \right)
$$

**Step 2: Simplify Each Term**

$$
6a^{2} \cdot \frac{1}{3 a^{2}} - 6a^{2} \cdot \frac{1}{a} = 6a^{2} \cdot \frac{1}{6 a^{2}}
$$

$$
2 - 6a = 1
$$

**Step 3: Solve for $$a$$**

$$
2 - 6a = 1
$$

Subtract 2 from both sides:

$$
-6a = -1
$$

Divide both sides by $$-6$$:

$$
a = \frac{1}{6}
$$

**Solution:**

$$
a = \frac{1}{6}
$$
$$ a = \frac{1}{6} $$

Solve:
The solution is
DONEID