(1) \( \frac{3^{x+1}-4 \cdot 3^{x-1}}{3^{x-2}} \)

To simplify the expression \( \frac{3^{x+1} - 4 \cdot 3^{x-1}}{3^{x-2}} \), we can start by rewriting \( 3^{x+1} \) and \( 3^{x-1} \) in terms of \( 3^{x-2} \). The term \( 3^{x+1} \) can be expressed as \( 3^{x-2} \cdot 3^3 \) (since \( x + 1 = (x - 2) + 3 \)). Thus, it becomes \( 27 \cdot 3^{x-2} \). Similarly, \( 4 \cdot 3^{x-1} \) can be written as \( 4 \cdot 3^{x-2} \cdot 3^1 = 12 \cdot 3^{x-2} \). So we can rewrite the original expression as: \[ \frac{27 \cdot 3^{x-2} - 12 \cdot 3^{x-2}}{3^{x-2}} \] Now we can factor out \( 3^{x-2} \) in the numerator: \[ = \frac{(27 - 12) \cdot 3^{x-2}}{3^{x-2}} = \frac{15 \cdot 3^{x-2}}{3^{x-2}} = 15 \] Thus, the simplified result is \( 15 \).