Both the Quantities have similar looking fraction but their denominators are bit different. As both are positive fractions so we just need to figure out whose denominator is smaller (=> Fraction is bigger). We also know that t > 1
=> \(2^t\) and \(3^t\) will be greater than 1
and \(3^t\) > \(2^t\) as 3 > 2 and t > 1
=> \(\frac{1}{3^t}\) < \(\frac{1}{2^t}\) [Property: In case of two +ve fractions with same numerator, the fraction with larger denominator is smaller ]
=> \(\frac{3}{3^t}\) < \(\frac{3}{2^t}\) [Property: Multiplying with a +ve number on both the sides of an inequality DOES NOT change the sign of the inequality]
=> 1 + \(\frac{3}{3^t}\) < 1 + \(\frac{3}{2^t}\)
=> \(\frac{1}{1+\frac{3}{3^t}}\) > \(\frac{1}{1+\frac{3}{2^t}}\)
=> Quantity B > Quantity A

So, Answer will be B
Hope it helps!