# When find LCD for a rational expressions.

Ok I have to find the Lowest Common Denominator for 3 ration expressions.
I dont 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
Homework Helper
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 isnt the only CD they have (x-2)?

dextercioby
Homework Helper
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 Im seriously not getting it.

dextercioby
Homework Helper
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 wouldnt 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
Homework Helper
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?

dextercioby