My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree2Thanks
  • 1 Post By v8archie
  • 1 Post By Denis
Reply
 
LinkBack Thread Tools Display Modes
April 26th, 2014, 07:33 PM   #1
Newbie
 
Joined: Apr 2014
From: Raleigh

Posts: 4
Thanks: 0

Smile 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!
clgordon is offline  
 
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
v8archie is offline  
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!!!!
clgordon is offline  
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.
clgordon is offline  
April 27th, 2014, 05:53 PM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,671
Thanks: 2651

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by clgordon View Post
Also, how'd you get your fractional expressions so neat? I'm jealous.
MathJax / Latex
v8archie is offline  
April 27th, 2014, 05:57 PM   #6
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,671
Thanks: 2651

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by clgordon View Post
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.
v8archie is offline  
April 27th, 2014, 07:52 PM   #7
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Quote:
Originally Posted by clgordon View Post
1 / (1+a^n) + 1 / (1+a^-n)
Let a = 1
1 / (1+1) + 1 / (1+1/1) = 1/2 + 1/2 = 1 ...hmmm
Thanks from agentredlum
Denis is offline  
April 28th, 2014, 03:57 AM   #8
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

We also must worry about certain values of a

$$a \ne 0 $$

$$a^n \ne -1$$

agentredlum is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
compound, express, simplify



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
simplify and express in cartesion notation Melody2 Complex Analysis 9 October 31st, 2013 07:18 PM
Express cos(4a) + sin(4a) using only cos(a) and sin(a) king.oslo Algebra 3 September 6th, 2013 12:09 PM
Express the function f o g* Shamieh Algebra 1 May 22nd, 2013 08:16 PM
Express as a product MathRaven Algebra 1 July 8th, 2012 03:17 PM
Express in a+bi form Singularity Complex Analysis 7 October 7th, 2010 07:06 AM





Copyright © 2019 My Math Forum. All rights reserved.