jmc

The common factor of 3 in the numerator and the common factor of 3 in the denominator will cancel: $$\frac{3^4+3^2}{3^3-3}=\frac{3(3^3+3^1)}{3(3^2-1)}=\frac{3^3+3^1}{3^2-1}$$ Now the numerator is $3^3+3=27+3=30$, and the denominator is $3^2-1=9-1=8$. Therefore, the fraction simplifies to $\frac{30}{8}=\boxed{\frac{15}{4}}$.