What is the simplified numerator for the given function?

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Discussion Overview

The discussion revolves around simplifying the numerator of a given function, focusing on the correct approach to factorization and reduction in the context of a homework problem.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about the question being asked regarding the numerator simplification.
  • Another participant confirms that the numerator has been correctly factored but emphasizes the need to divide out common factors with the denominator.
  • A participant suggests that the simplified numerator could be 12x^2 + 4, indicating they are nearing completion of their homework attempt.
  • A later reply reiterates the suggestion of 12x^2 + 4 and proposes a further reduction to 4(3x^2 + 1), expressing uncertainty about the acceptance of either form by homework software.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which form of the numerator is preferred or accepted by the homework software, indicating multiple views on the simplification process.

Contextual Notes

There is an unresolved question regarding the acceptance of different forms of the numerator by the homework software, and the discussion does not clarify the implications of this on the overall problem-solving approach.

hannahSUU
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View attachment 7529

I have most of this question figured out, but I don't understand what this one question is asking? Anyone know?

thanks <3
 

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You've correctly factored the numerator, but you still need to divide out any factors in common with the denominator...
 
MarkFL said:
You've correctly factored the numerator, but you still need to divide out any factors in common with the denominator...

So my answer would just be 12x^2 + 4? I'm on my last attempt
 
hannahSUU said:
So my answer would just be 12x^2 + 4? I'm on my last attempt

Yes, I would reduce this to (and factor the numerator a bit more):

$$f''(x)=\frac{4\left(3x^2+1\right)}{\left(x^2-1\right)^3}$$

I have no idea whether your homework software will accept both $12x^2+4$ and $4\left(3x^2+1\right)$, but I would prefer the latter if working the problem myself.
 

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