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Math Help - Index Laws

  1. #1
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    Index Laws

    Hello

    Here's the problem I need a hand with, I need to simplify it:

    (3^2n + 5x3^n + 6)/(3^n + 3)

    Thanks in advance, all help is really appreciated
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  2. #2
    o_O
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    Recall that: a^{bc} = \left(a^b\right)^c

    \frac{3^{2n} + 5\cdot 3^n + 6}{3^n + 3} = \frac{\left({\color{blue}3^n}\right)^2 + 5\cdot {\color{blue}3^n} + 6}{{\color{blue}3^n} + 6}

    Now it might be hard to see but the numerator essentially resembles a quadratic that you can factor. To see, let \color{blue} x = 3^n.

    This yields: \frac{{\color{blue}n}^2 + 5{\color{blue}n} + 6}{{\color{blue}n} + 6}

    Can you do it now?
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