Algebra Pre-Algebra and Basic Algebra Math Forum

 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 step-by-step 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*} Thanks from agentredlum 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
Quote:
 Originally Posted by clgordon Also, how'd you get your fractional expressions so neat? I'm jealous. MathJax / Latex 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
Quote:
 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, 08:52 PM   #7
Math Team

Joined: Oct 2011

Posts: 14,597
Thanks: 1039

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, 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 $$a \ne 0$$ $$a^n \ne -1$$  Tags compound, express, simplify Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Melody2 Complex Analysis 9 October 31st, 2013 08:18 PM king.oslo Algebra 3 September 6th, 2013 01:09 PM Shamieh Algebra 1 May 22nd, 2013 09:16 PM MathRaven Algebra 1 July 8th, 2012 04:17 PM Singularity Complex Analysis 7 October 7th, 2010 08:06 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      