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April 26th, 2014, 08:33 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 stepbystep on how to simplify this compound expression. Thanks! 
April 26th, 2014, 08:42 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,697 Thanks: 2681 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*} 
April 26th, 2014, 09:50 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, 10:10 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, 06:53 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,697 Thanks: 2681 Math Focus: Mainly analysis and algebra  
April 27th, 2014, 06:57 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,697 Thanks: 2681 Math Focus: Mainly analysis and algebra  
April 27th, 2014, 08:52 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  
April 28th, 2014, 04:57 AM  #8 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 
We also must worry about certain values of a $$a \ne 0 $$ $$a^n \ne 1$$ 

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compound, express, simplify 
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