9⋅3n+1−3n+23n+1−3n\frac{9 \cdot 3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}3n+1−3n9⋅3n+1−3n+2
= 3n⋅3n⋅31⋅−32⋅323n⋅31−3n\frac{3^n \cdot 3^n \cdot 3^1 \cdot -3^2 \cdot 3^2}{3^n \cdot 3^1 - 3^n}3n⋅31−3n3n⋅3n⋅31⋅−32⋅32
= 3n(32⋅31)3n(31−1)\frac{3^n (3^2 \cdot 3^1)}{3^n (3^1 - 1)}3n(31−1)3n(32⋅31)
= 27−93−1\frac{27-9}{3-1}3−127−9
= 182\frac{18}{2}218
= 9
