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 April 26th, 2014, 07:33 PM #1 Newbie   Joined: Apr 2014 From: Raleigh Posts: 4 Thanks: 0 Simplify Compound Express 1/1+a^n + 1/1+a^-n I know what the answer is, but, if you'd be so kind, I'd like a step-by-step on how to simplify this compound expression. Thanks!
 April 26th, 2014, 07:42 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra \begin{align*} \frac{1}{1+a^n} + \frac{1}{1+a^{-n}} &= \frac{1}{1+a^n} + \frac{a^n}{a^n}\cdot\frac{1}{1+a^{-n}} \\ &= \frac{1}{1+a^n} + \frac{a^n}{a^n + 1} \\ &= \frac{1+a^n}{1+a^n} \\ &= 1 \end{align*} Thanks from agentredlum
 April 26th, 2014, 08:50 PM #3 Newbie   Joined: Apr 2014 From: Raleigh Posts: 4 Thanks: 0 So, you're using the identity property in order to remove the negative variable exponent. Very good. I was changing the second term into a complex fraction in order to remove the negative exponent:1/1/a^n. So, I was making the expression this: 1/1+a"n + 1/1/a^n, and then I was working on the denominator to find the LCD of the denominator a^n, and then multiplying each term's denominator until it wasn't complex anymore. However, I forgot to multiply the numerator by a^n, too. Essentially, I was multiplying the fractional terms by 1/a^n, as opposed to a^n/a^n, which is equal to one, which, essentially, doesn't change the value of the expression. I think that was my mistake. Correct me if I'm wrong. Thanks, again!!!!
 April 26th, 2014, 09:10 PM #4 Newbie   Joined: Apr 2014 From: Raleigh Posts: 4 Thanks: 0 Also, how'd you get your fractional expressions so neat? I'm jealous.
April 27th, 2014, 05:53 PM   #5
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Quote:
 Originally Posted by clgordon Also, how'd you get your fractional expressions so neat? I'm jealous.
MathJax / Latex

April 27th, 2014, 05:57 PM   #6
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 Originally Posted by clgordon I think that was my mistake. Correct me if I'm wrong.
I don't really understand what you were up to, but forgetting to multiply the numerator by a factor you use on the denominator would be a problem.

April 27th, 2014, 07:52 PM   #7
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Quote:
 Originally Posted by clgordon 1 / (1+a^n) + 1 / (1+a^-n)
Let a = 1
1 / (1+1) + 1 / (1+1/1) = 1/2 + 1/2 = 1 ...hmmm

 April 28th, 2014, 03:57 AM #8 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 We also must worry about certain values of a $$a \ne 0$$ $$a^n \ne -1$$

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