Can I Simplify This Algebraic Expression by Canceling Out the h?

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The discussion revolves around simplifying the algebraic expression -2rh - h^2 + 2r/h. It is clarified that the expression cannot be simplified by canceling out the variable h because it is not present in all terms of the numerator. Instead, the expression can be split into two fractions for further simplification. Additionally, if this expression is part of a difference quotient, taking the limit as h approaches 0 poses a problem unless the numerator also equals zero at that point. Overall, the consensus is that cancellation is not valid in this case.
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I'm trying to simplify -2rh-h^2+2r/h

can I simplify this anymore by canceling out the h, or is that not correct. Also, I don't believe I can factor out the h in the numerator because it's not in all 3 on top, is that correct?
 
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vt33 said:
I'm trying to simplify -2rh-h^2+2r/h

can I simplify this anymore by canceling out the h, or is that not correct. Also, I don't believe I can factor out the h in the numerator because it's not in all 3 on top, is that correct?

Yes,it cannot be factored,since it's missing from one of the terms of the sum.
However,it can be split into 2 fractions and "symplified"...

Daniel.
 
Assuming you mean \frac{-2rh- h^2+ 2r}{h}, then, yes, you cannot simplify by cancelling. If this is a difference quotient and you want to take a limit as h goes to 0 then you have a problem! That limit will only exist if the numerator is also 0 when h= 0.
 
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