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To simplify \( \frac{3^{x+1}-4 \cdot 3^{x-1}}{3^{x-2}} \), start by factoring out powers of 3 in the numerator. The expression in the numerator can be rewritten as: \[ 3^{x+1} - 4 \cdot 3^{x-1} = 3^{x-1}(3^2 - 4) = 3^{x-1}(9 - 4) = 3^{x-1} \cdot 5 \] Now substituting this back into our original expression gives: \[ \frac{3^{x-1} \cdot 5}{3^{x-2}} = 5 \cdot \frac{3^{x-1}}{3^{x-2}} = 5 \cdot 3^{(x-1) - (x-2)} = 5 \cdot 3^{1} = 15 \] So the simplified form of the expression is \( 15 \).