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Friday, November 25, 2005

Simplifying Rational Expressions

Why hello there, my one and only favorite pre cal class, of all you smart smart people. I am the scribe for today. I must start off with mentioning how very sorry I am for messing up the whole blog thing. I was at ChoralFest that day, and what not. I am very sorry for messing it up. I promise it shall never happen again.
Now that we got that out of the way...

Todays class started off with Mr.K being exactly three minutes late for class. *Shakes finger* tsk tsk Mr. K, you should know better. Haha, just kidding.

Mr.K tried to show us how to create a del.icio.us account. If you have any problems with it, I would suggest asking one of your classmates who has already done the task. It's quite easy once you know what you are doing. Then, he showed us how to tag a site that we think is useful. That is also rather easy, but yet again, if you have trouble, I would suggest talking to a classmate about it. You can even ask me, because I have done it before.

Then we started getting down to the really important stuff. We learned about simplifying rational expressions. Mr.K wrote the following on the board: 2+4/2 (by the way the / means division). He asked us how we would solve/simplify the problem. Most of us said we would add the 2 and the 4 first, and then divid by two, which would give us (2+4=6, 6/2=3) 3. This is the RIGHT way to solve it. Some people look at the problem and think that the twos reduce, resulting in four. Which is WRONG. As Mr. K says, "No no no no no no no no no no no no no no..." (you get the picture).

Why you ask? Well, because there are really brackets on both sides of the numerator and the denominater, even though they may not be written. Therefore, you know that you add before you divide. Remember that according to Mr.K, "Six of you are going to do this wrong!" So, "Prove me wrong!" Remember that.

So, now if we are given the same equation, but with a variable in it, for example (2+4x/2)...it DOES NOT equal 4x, because thats WRONG, but rather you factor out the 2, giving you 2(1+2x)/2 which then reduces to 1+2x.

"So why does it reduce this time, but not in the beginning? Well, because this time the 2 has been factored out, which means it no longer belongs in the bracket.

But, for example, if you are given a problem like (x+3/2), there are no common factors, so the rational expression cannot be simplified.

Making the expressions a little more complicated, we are given (x^2+3x/2x). We factor out the x in the numerator, giving us x(x+3)/2x. Becuase the x in the numerator is outside the bracket, it reduces with the x in the denominater., resulting in x+3/2, which is the same as x/2+ 3/2, which is also, y=1/2x+3/2. Look familiar? Yes. These rational expressions can also be equations of lines, and can be drawn out on a graph.

The second last question we did was x^2-5x-6/x-6. We factor this, which gives us (x-6)(x+1)/(x-6). The (x-6) and the (x-6) reduce, giving us x+1, which is the same as y=x+1.

That last question given was x^2-3x-10/x^2-4. We factor this out to get (x-5)(x+2)/(x-2)(x+2). Both the (x+2) and the (x+2) reduce, resiulting in (x-5)/(x-2).

Just remember: No denominater can equal O! Why? Because it would then be undefined, and not be a RATIONAL expression.

Homework for tonight is Exercise 42, omit #12. The next scribe is SAMUS !!!! good luck Sammy!

Thats it! Thats the whole ball of wax!


At 11/25/2005 10:01 PM, Blogger Darren Kuropatwa said...

Outstanding scribe Kristen!

In the fifth paragraph from the bottom you wrote:
The (x-6) and the (x-6) reduce, giving us x=1, which is the same as y=x+1.

That "x=1" should be "x+1"

I make that same typo all the time myself. ;-)

I really liked the personal touch you added to your post -- it made it really enjoyable to read. ;-)

At 11/26/2005 11:25 AM, Anonymous Anonymous said...

awwwww, boo-who T____T

At 11/27/2005 8:45 PM, Anonymous Anonymous said...

mr kuropatwa took away an editor's initiative chance from this post. >:O

At 11/27/2005 9:12 PM, Blogger Darren Kuropatwa said...

Not really.

I wouldn't have approved that minor typo as an Editor's Initiative candidate. ;-)


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