Question

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

Explanation:

Step1: Eliminate denominators

Multiply all terms by $6a^2$ (the least common denominator of $3a^2$, $a$, and $6a^2$) to clear fractions:
$$6a^2 \cdot \frac{1}{3a^2} - 6a^2 \cdot \frac{1}{a} = 6a^2 \cdot \frac{1}{6a^2}$$
Simplify each term:
$$2 - 6a = 1$$

Step2: Isolate the variable term

Subtract 2 from both sides to isolate the term with $a$:
$$-6a = 1 - 2$$
Simplify the right-hand side:
$$-6a = -1$$

Step3: Solve for $a$

Divide both sides by $-6$ to solve for $a$:
$$a = \frac{-1}{-6} = \frac{1}{6}$$

Answer:

$\frac{1}{6}$