<s>[INST] How to simplfy this indices question Grade 10 :$\frac{3^n-4 \cdot 3^{n-2}}{3^{n+1}-3^{n-1}}$ I am a student in grade 10 and i was given this question about indices 
$$\frac{3^n-4 \cdot 3^{n-2}}{3^{n+1}-3^{n-1}}$$
All I am capable to do is expanding it out, i.e. from $3^{n-2}$ to $3 \cdot 3^{-2}$. I am unable proceed to the next step, please show step by step solution! Thank you!
 [/INST] Welcome. You can write:
$3^n-4\times 3^{n-2}=3^n-3^{n-2}-3\times 3^{n-2}$
$3^{n+1}-3^{n-1}=3(3^n-3^{n-2})$
Then the fraction(F) reduces as follows:
$F=\frac{1}{3}-\frac{1}{3^{2-n}}\times(\frac{1}{3^{n+1}-3^{n-1}})=\frac{1}{3}-\frac{1}{8}=\frac {5}{24}$
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