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Thread: Solve really fast anyone?

  1. #1
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    Solve really fast anyone?

    $\displaystyle (a^2n-a^n-6)/(a^n+8)$

    Divide.
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  2. #2
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    Quote Originally Posted by A Beautiful Mind View Post
    $\displaystyle (a^2n-a^n-6)/(a^n+8)$

    Divide.
    Synthetic division:

    -8 | 1 -1 -6
    __| 0 +8 +56
    ___1__7__50

    1*a^n + 7 + 50/(a^n+8)
    = a^n + 7 + 50/(a^n+8)

    You can do it with long division as well.

    idk the easy way for formatting
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  3. #3
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    Hello, A Beautiful Mind!

    Is there a second typo?
    The problem would make more sense . . .



    Divide: .$\displaystyle \frac{a^{2n}-a^n-6}{a^{{\color{red}3}n}+8}$

    Factor: .$\displaystyle \frac{(a^n+2)(a^n-3)}{(a^n+2)(a^{2n}-2a^n + 4)} $


    Reduce: .$\displaystyle \frac{a^n - 3}{a^{2n} - 2a^n + 4} $

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  4. #4
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    Second typo?

    I only edited my first post to say divide, lol.

    $\displaystyle I found that the answer is: a^n - 9 + 66/a^n+8...just don't know how to get there.$
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  5. #5
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    Yes, the first typo was the exponent "2n" . . .


    You have: .$\displaystyle (a^{{\color{red}2n}} - a^n - 6) \div (a^n + 8)$


    Long division:

    . . $\displaystyle \begin{array}{cccccccc}
    &&&& a^n & - & 9 \\
    & & -- & -- & -- & --& -- \\
    a^n + 8 & ) & a^{2n} & - & a^n & - & 6 \\
    & & a^{2n} & + & 8a^n \\
    & & -- & -- & -- \\
    & & & - & 9a^n & - & 6 \\
    & & & - & 9a^n & - & 72 \\
    & & & -- & -- & -- & -- \\
    & & & & & & 66 \end{array}$


    Answer: .$\displaystyle a^n - 9 + \frac{66}{a^n+8}$

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