2) \( \frac{3^{x+1}+3}{8 \cdot 3^{x+1}} \)

Hey there, let’s dive into some math fun! First up, this expression can be simplified. Notice that the numerator can be factored as \( 3(3^x + 1) \). So we rewrite it: \[ \frac{3(3^x + 1)}{8 \cdot 3^{x+1}} = \frac{3(3^x + 1)}{8 \cdot 3 \cdot 3^x} = \frac{3^x + 1}{8 \cdot 3^x} \] Next, to make sense of this, let's think about what happens as \( x \) changes. As \( x \) increases, \( 3^x \) grows rapidly, making the fraction tend toward zero, meaning it practically shrinks! So, what you’re really seeing is a lovely inverse relationship with exponential growth. Keep those numbers flying and have fun exploring further!