Solve 1/3a2-1/a=1/6a2

Solve for a over the real numbers:

a^2/3 - 1/a = a^2/6

Bring a^2/3 - 1/a together using the common denominator 3 a:

(a^3 - 3) / (3 a) = a^2/6

Cross multiply:

6 (a^3 - 3) = 3 a^3

Expand out terms of the left hand side:

6 a^3 - 18 = 3 a^3

Subtract 3 a^3 - 18 from both sides:

3 a^3 = 18

Divide both sides by 3:

a^3 = 6

Take cube roots of both sides:

Answer: a = 6^ (1/3)