When find LCD for a rational expressions.

[DLxX]

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?

 

[dextercioby]

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.

 

[DLxX]

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)?

 

[dextercioby]

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.

 

[DLxX]

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.

 

[dextercioby]

It would really matter for you to know/understand why the answers is the one that it is,namely x^{2}-4.

Daniel.

 

[DLxX]

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?

 

[dextercioby]

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.

 

[DLxX]

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?

 

[dextercioby]

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.