Simplifying Difference Quotients

jordeng55

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Jan 20, 2019
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Hey guys, taking Calc 1 and having some issues solving something that's likely very easy. As you can see in the attachments, I'm working on difference quotients. It wants me to simplify and rationalize. I know I can rationalize this (although I don't really understand why I would want to since we usually rationalize the denominator), but I can't seem to simplify it anymore. Maybe I'm just forgetting some of the rules of square roots?

Anyway, any help would be appreciated! Thanks in advance for your time :)
 

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  • Simplify or rationalize differene quotient.jpg
    Simplify or rationalize differene quotient.jpg
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Hey guys, taking Calc 1 and having some issues solving something that's likely very easy. As you can see in the attachments, I'm working on difference quotients. It wants me to simplify and rationalize. I know I can rationalize this (although I don't really understand why I would want to since we usually rationalize the denominator), but I can't seem to simplify it anymore. Maybe I'm just forgetting some of the rules of square roots?

Anyway, any help would be appreciated! Thanks in advance for your time :)
attachment.php


What do you get after rationalizing the numerator? Please share with us!
 
Solved!

I tried to just submit after rationalizing and it was right! So I suppose I couldn't or at least didn't need to simplify... Here's the 'solution' or at least why my instructor wanted.

(h+2x) / sqrt(((x+h)^2)+12) + sqrt(x^2+12)

Maybe this can help someone in the future :)
 
I tried to just submit after rationalizing and it was right! So I suppose I couldn't or at least didn't need to simplify... Here's the 'solution' or at least why my instructor wanted.

(h+2x) / sqrt(((x+h)^2)+12) + sqrt(x^2+12)

Maybe this can help someone in the future :)

Actually, you did simplify, didn't you? You divided the numerator and denominator by h, resulting in an expression that is defined when h=0. That's all the simplifying that matters.

But your point is a good one: When a problem looks complicated, and even the answer looks ugly, just do what you can! If nothing more can be done, that's fine. Not everything ends up as tidy as the problems you learned early in the study of algebra.
 
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