What is the simplified numerator for the given function?

  • MHB
  • Thread starter hannahSUU
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In summary, the conversation is discussing how to correctly factor and divide out common factors in a given equation. The final answer is either 12x^2 + 4 or 4(3x^2 + 1).
  • #1
hannahSUU
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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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  • #2
You've correctly factored the numerator, but you still need to divide out any factors in common with the denominator...
 
  • #3
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
 
  • #4
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):

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

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.
 

FAQ: What is the simplified numerator for the given function?

What is a simplified numerator?

A simplified numerator is the number written above the fraction line in a fraction. It is usually smaller than the denominator and does not have any common factors with it.

Why is it important to simplify the numerator?

Simplifying the numerator makes fractions easier to work with and understand. It also helps to find equivalent fractions and perform operations on fractions.

What are the steps to simplify a numerator?

To simplify a numerator, you need to find the greatest common factor (GCF) between the numerator and denominator and divide both by it. Then, you can reduce the fraction to its simplest form.

Can a numerator be simplified to 1?

Yes, a numerator can be simplified to 1 if the numerator and denominator are the same number. This means that the fraction is equivalent to 1 and is already in its simplest form.

Can the numerator be larger than the denominator?

Yes, the numerator can be larger than the denominator. This type of fraction is called an improper fraction. However, it can still be simplified by dividing both the numerator and denominator by their GCF to get a proper fraction.

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