Answer:
the solution to the equation is a = -1/4.
Explanation:
To solve the given equation:
1/3a^2 - 1/a = 1/6a^2
We want to find the value of "a" that satisfies the equation.
To begin, let's simplify the equation by getting rid of the fractions. We can do this by multiplying each term by the common denominator, which in this case is 6a^2.
Multiplying each term by 6a^2, we have:
(6a^2)(1/3a^2) - (6a^2)(1/a) = (6a^2)(1/6a^2)
Simplifying further, we get:
2a - 6a = 1
Combining like terms, we have:
-4a = 1
Next, we want to isolate "a" by dividing both sides of the equation by -4.
Dividing by -4, we get:
a = 1/(-4)
Simplifying further, we have - a = -1/4
Therefore, the solution to the equation is a = -1/4.
In conclusion, the value of "a" that satisfies the equation 1/3a^2 - 1/a = 1/6a^2 is a = -1/4.