SOLUTION: Simplify {[3^(2n)] - 1} / {[3^(n+1)] - 3}. Thank you :)

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Question 1126069: Simplify {[3^(2n)] - 1} / {[3^(n+1)] - 3}. Thank you :)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Simplify: %28%283%5E%282n%29%29+-+1%29+%2F+%28%283%5E%28n%2B1%29%29+-+3%29

The numerator factors as the difference of squares:

3%5E%282n%29-1+=+%283%5En-1%29%283%5En%2B1%29

In the denominator, take one factor of 3 out of "3^(n+1)"; then factor out the common factor of the two terms:

3%5E%28n%2B1%29-3+=+3%283%5En%29-3+=+3%283%5En-1%29

Now simplify: