x^4-1/(x-1)?

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A few days ago

missevav

Favorite Answer

First, we need to factor the numerator. Notice that (x^4 – 1) is the difference of 2 perfect square. Thus,

(x^4 – 1) = (x^2 – 1) (x^2 + 1)

Let’s take a closer look at that first factor.

(x^2 – 1) is also a difference of 2 perfect squares. So,

(x^2 – 1) = (x – 1) (x + 1)

Now we can rewrite our problem with our factors.

(x – 1)(x + 1)(x^2 + 1)

________________

(x – 1)

We have common factors in the numerator and denominator, so we can remove them.

Final Answer:

(x + 1) (x^2 + 1)

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