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Am I correct in stating that if $\frac{x^n}{x^{n-1}}=\frac{x^n}{x^n\cdot x^{-1}}=\frac{1}{x^{-1}}=x$ then $\begin{align*} \left|\frac{(x^2-5x+2)^n}{2^{n+1}}\cdot\frac{2n}{(x^2-5x+2)^{n-1}}\right|&=\left|\frac{(x^2-5x+2)^n}{(x^2-5x+2)^{n-1}}\cdot\frac{2n}{2^{n+1}}\right|\\\\ &\neq\left|(x^2-5x+2)\right|\frac{1}{2} \end{align*}$

This would have been true if the second term was: $\frac{2^n}{2^{n+1}}$ and not $\frac{2n}{2^{n+1}}$

I'm trying to confirm that my textbook has a typo to make sure I am not screwing something up in the math.

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    @AsafKaragila: I think edits overlapped there or something weird happened, I recall I didn't add the $(algebra)$ tag, I don't know why it says I did. I was unaware of the fact, thank you for pointing that out.2012-05-03

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With the structure of the problem as you've given it, if the supposed answer is $\left|(x^2-5x+2)\right|\frac{1}{2}$, I'd agree that the $2n$ should have been $2^n$.