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Factor the difference of squares $x^4-1$ as the product of two conjugated binomials
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$\lim_{x\to1}\left(\frac{\left(x^{2}+1\right)\left(x^{2}-1\right)}{x^6-1}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(1)lim((x^4-1)/(x^6-1)). Factor the difference of squares x^4-1 as the product of two conjugated binomials. We can factor the polynomial x^6-1 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -1. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^6-1 will then be.