Question

x^4 + 1
------- = ?
x^2 - 1

Answer 1

Are you sure the question isn't?
\[\frac{x^4-1}{x^2-1}\]

Answer 2

yes, thats it

Answer 3

We know
\[a^2-b^2=(a+b)(a-b)...............................(1)\]
here we have,
\[\frac{x^4-1}{x^2-1}\]
Now we'll use (1) to factor the numerator
\[x^4-1=(x^2-1)(x^2+1)\]
so we have
\[\frac{(x^2-1)(x^2+1)}{x^2-1}\]
Let's cancel the common terms from numerator and denominator
\[\frac{\cancel {(x^2-1)}(x^2+1)}{\cancel{x^2-1}}\]
We get finally
\[{x^2+1}\]

Answer 4

what if we had an \[x^{4}+1\] in the numerator? could you solve that for me?

Answer 5

Then it can't be reduced further:(

Answer 6

alright then... thanks for the help! :)

Answer 7

You're welcome:)
Welcome to Open Study:)