2) \( \frac{9^{x}-3^{x}-6}{3^{x}-3} \)

Let's rewrite the expression in a more manageable form. Notice that \( 9^x = (3^2)^x = (3^x)^2 \). So, let \( y = 3^x \). Then, the expression becomes: \[ \frac{y^2 - y - 6}{y - 3} \] Now, we need to factor the numerator \( y^2 - y - 6 \). This factors into \( (y - 3)(y + 2) \). Thus, our expression simplifies to: \[ \frac{(y - 3)(y + 2)}{y - 3} \] As long as \( y \neq 3 \) (or \( 3^x \neq 3 \)), we can cancel \( y - 3 \): \[ y + 2 \] Substituting back \( y = 3^x \): \[ 3^x + 2 \] So, the simplified form of the expression is \( 3^x + 2 \).