MHB What is the simplified numerator for the given function?

[hannahSUU]

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

 

[MarkFL]

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

 

[hannahSUU]

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

 

[MarkFL]

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.