A few days ago
x^4-1/(x-1)?
x^4-1/(x-1)?
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A few days ago
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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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