Paul's Online Math Notes

Notice
If you were affected by the server issues last night I apologize. Over the years the traffic on the site has increased significantly and it's reaching the point that my server is having issues handling the heavy traffic that comes at the end of the semester. Luckily I've got a new more powerful server setup almost ready to go that should be able to handle the increased traffic for the foreseeable future. It is currently scheduled to "go live" on Wednesday, May 11 2016 at 10:30 Central Standard Time. Unfortunately this is the earliest possible day to do the switch over between servers.

In the mean time the website is liable to be somewhat unreliable during the peak usage times at night and for that I apologize.

Paul.
May 5, 2016

Algebra/Trig Review
 Next Chapter Trigonometry Factoring Previous Section Next Section Graphing and Common Graphs
Simplifying Rational Expressions

Simplify each of the following rational expressions.

1.

Show Solution

There isn’t a lot to these problems.  Just factor the numerator and denominator as much as possible then cancel all like terms.  Recall that you can only cancel terms that multiply the whole numerator and whole denominator.  In other words, you can’t just cancel the  and you can’t cancel a 4 from the 8 in the numerator and the 4 in the denominator.  Things just don’t work this way.

If you need convincing of this consider the following number example.

Here is the answer to this problem.

2.

Show Solution

In this one you’ve got to be a little careful.  First factor the numerator and denominator.

At first glance it doesn’t look like anything will cancel.  However remember that

Using this on the term in the denominator gives the following.

Also recall that

so it doesn’t matter where you put the minus sign.

 Factoring Previous Section Next Section Graphing and Common Graphs Next Chapter Trigonometry

 © 2003 - 2016 Paul Dawkins