The phrasing in this question ("is closest to") is meant to hint that we can avoid an exact calculation.
From the answer choices, we can see that the denominator is going to be bigger than the numerator, so we have to think about how those two values really relate to one another....
Since X = 10^10, we know that we're dealing with a BIG number
The numerator gives us X^2 and the denominator gives us 3(X^2)
(10^10)^2 = 10^20 which is A LOT BIGGER than 10^10
Here they are, for context:
10^10 = 10,000,000,000
10^20 = 100,000,000,000,000,000,000
3(10^20) = 300,000,000,000,000,000,000
10^20 and 3(10^20) are so much bigger than the other "elements" in the numerator and denominator that those other elements are "negligible" (by comparison) to the overall calculation.
This means that we're basically dealing with (X^2 + a little)/(3X^2 - a little). That fraction is approximately 1/3
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