Reducing a Complex Algebraic Fraction
by: Clara Stone
In this lesson we are going to simplify a complex algebraic fraction.
First, here is the syntax we will use for algebraic expressions ? so-called 'one-line' notation, that uses common keyboard operations such as ,-,*,/ and ^. If you find this syntax a little cumbersome, cut and paste any of these expressions to a 'syntax converter' located at this algebra resources page: http://www.algebra1help.com/links. It will create a nice looking textbook notation.
When we refer to a ?complex? fraction in algebra, we don?t really mean ?complicated?, rather it is a fraction that has another fraction in its numerator or denominator (or both). So, here is our problem:
(x-y)^2/((x y)/(x^2-y^2))
Notice that the denominator is another fraction. The first thing we need to do is simplify the fraction in the denominator (there is nothing to simplify in the numerator). We start by factoring the denominator (of the denominator):
(x-y)^2/((x y)/((x-y)*(x y)))
We have employed a simple ?difference of two squares? identity. Notice that now one of the factors in the numerator, (x y) is also found in the denominator. That means that we can reduce them. Since that was the only factor in the numerator, we replace it by ?1?:
(x-y)^2/(1/(x-y))
Now we are going to replace the main fraction line with the division symbol : (imagine that there is a line between the dots!)
(x-y)^2:(1/(x-y))
Once we got rid of the complex fraction, we can convert the division into multiplication. This is done by ?flipping? the numerator and denominator of the second fraction according to the following rule a/b:c/d=a/b*d/c. Since in our case ?c? is equal to 1, we can simply leave it out, once it becomes denominator:
(x-y)^2*(x-y)
The rest is a simple multiplication problem ? we just need to add the numeric exponents (?1? is implied):
(x-y)^(2 1)
Which gives us the final result:
(x-y)^3
This wasn?t that ?complex?, was it?
Stay tuned for more simple algebra lessons!
About The Author
Clara Stone is the principal content developer for Algebra Toolkit (www.algebra-help.org), a software program that produces solution steps and explanations for any algebra problem entered by the ustudent. In her spare time she tutors algebra to high school and college students.
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The Practice of Ergonomics
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by: Bo Pritchard
How can you apply ergonomics to your work life?
Thanks to the study of ergonomics, we can now find better ways to work. It has been shown that our bodies can be under stress and tension even when we are sitting at a desk. Applying the techniques learned through the study of the work environment helps the body to work better and more efficiently.
Often, there are simple changes to the way people sit and move that can really help relieve tension. Something as simple as where the computer monitor is positioned can make such a difference. These techniques are easy to apply; all it takes is a little knowledge.
Applying Ergonomics to Every Day Life
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The Practice of Ergonomics
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Oh, to be able to breeze through a brand new piece without all the stops and starts!
What you may not realize is that sight-reading is an art in itself, separate and apart from pianistic ability.
Many conservatory musicians, even many soloists, are not the great sight-readers you might expect.
Sight-reading is a special craft within the art of music that won?t come automatically.
You must work at it just as you work at technique, or interpretation.
You could have the technique of a Horowitz on the keyboard, or a Segovia on the guitar, but still be a laughable sight-reader.
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Keyboard > How To Become A Better Sight-Reader
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As an example: on Monday 12th December 2005, I wanted to buy a copy of Jamie Oliver's new cook book Jamie's Italy from amazon.co.uk. So, I went to the ?Books? section of their website and searched for ?olivers italy? and these 9 items appeared on the results page:
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How To Improve Your Site Search
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In the past I?ve never really paid much attention to security issues when it comes to user names and passwords. Frankly I figured it was all a lot of overblown hype. This led to an unfortunate incident that involved my website being attacked, apparently by a skillful youth with a propensity for mischief.
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Securing Your Accounts With Well-Crafted Passwords
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With the exception of those who are competing in reality TV shows, who wants to be watched?
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Keyboard > The Spy Who Robbed Me: What You Need To Know About Spyware
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Let?s start with your computer table. Its size may vary depending on your design. It may be wide enough to accommodate two ?bulky? PC sets, or it could barely hold one, and you don?t have enough space left for the keyboard or the mouse.
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Is Your PC Crowding Your Desk?
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Hard Work!
by: Robert J Farey
MAKE A MILLION $ PER MONTH.
No work involved.
Do it whilst sitting on the beach at Maliboo.
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The trouble is that so many newcomers to the internet get taken in by this sort of hype. No wonder that so many get disillusioned and wrap up and go away never to return.
It is a real pity that this sort of thing is allowd to happen. If only people would tell the truth they would get a far better response to their adverts.
Tell it as it is.
With the right information and a little incentive it is possible to start a business working from home, using nothing more than a desktop computer and something to sell.
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Just a minute!
What do we mean by 'hard work'?
Sitting...
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How To Choose Which Web Development Package Is Right For You
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by: Andrew Smith
There are plenty of options when it comes to web site creation software and a wannabe web designer might have a hard time deciding which to choose. We will have a look at the most popular web creation programs: Front Page, Dreamweaver and Adobe GoLive. All three offer a user-friendly interface and plenty of beginner and advanced options that will allow you to create the website of your dreams. A large majority of website hosting companies accept the final outputs of the three programs, but you will still need to check your web page for compatibility with different web browsers.
Front Page
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Keyboard > How To Choose Which Web Development Package Is Right For You
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Having an appropriate home business office is just as important as your business itself. Many factors affect how you approach your work at home business including distractions, proper office equipment and the overall environment of your business office.
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Your Home Business Office Keyboard patio furniture Reducing a Complex Algebraic Fraction
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Prom And Homecoming Dresses For The 2006 Season silk Keyboard Reducing a Complex Algebraic Fraction
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