MHB What is the simplified numerator for the given function?

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The discussion centers on simplifying the numerator of a function by factoring and reducing it against the denominator. Participants confirm that while the initial numerator, 12x^2 + 4, is factored correctly, it can be further simplified to 4(3x^2 + 1). There is uncertainty about whether homework software will accept both forms of the answer. The preferred final answer for clarity and simplicity is the more factored version. The conversation emphasizes the importance of reducing common factors in mathematical expressions.
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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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