When find LCD for a rational expressions.

AI Thread Summary
To find the Lowest Common Denominator (LCD) for the rational expressions with denominators x^2 - 4 and x - 2, the correct LCD is x^2 - 4, not just x - 2. The process involves factoring the denominators and identifying the smallest common multiple of all factors. Simply multiplying the denominators without considering their common factors may lead to incorrect conclusions. It's essential to include all distinct factors from the denominators while ensuring common factors are counted only once. Understanding this concept helps clarify how to determine the correct LCD for similar problems.
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Ok I have to find the Lowest Common Denominator for 3 ration expressions.
I don't think the numerators are important so Ill just leave them out. The denominators are

x^2 - 4 and x -2 I got the LCD as x-2. correct?

When finding the LCD in expressions like this you just have to factor and pick the term that they both have in common right?
 
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Nope,u have to pick just that:the lowest common denominator.Think of the numbers:what is the lowest common multiple of 6 and 3...?Is it 3??

Daniel.
 
Well the first one comes out to (x-2) and (x+2) while the 2nd one just stays as (x-2). So isn't the only CD they have (x-2)?
 
No,because the common denominator has to be a common multiple of the "old" denominators...That's why i gave the example with the numbers...Instead of #,you have polynimials...

Daniel.
 
Would you mind just giving me the answer for the one I mentioned? I have 3 more problems just like it and right now I am seriously not getting it.
 
It would really matter for you to know/understand why the answers is the one that it is,namely x^{2}-4.

Daniel.
 
Ok I think I get it now. You take x-2 from the first one and x-2 from the 2nd one and multiply them right? But wouldn't that end up x^2 -4x + 4? Why do I take the x+2 from the first one?

EDIT: I take all the DIFFERENT factors right? So that they each get a part?
 
Nope,it has to be the smallest common denominator,as i said the smalles common MULTIPLE OF THE 2 DENOMINATOS.The smallest one for x^{2}-4 is x^{2}-4 and that's that...

That simple multiplication between the denominators would be valid if the 2 polynomials would be prime one wrt another,which is not the case in here...

Daniel.
 
So I can essentially just multiply the 2 denominators of any problem like this and still get the correct answer? Or factor out the 2 denominators and multiply all the factors with each other, crossing out all the factors that were in both?
 
  • #10
Yes,you finally got it...That "crossing out" doesn't mean eliminating,just "counting" only once in the product,okay?
In your case,you'd have to count "x-2" only once.

Daniel.
 

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