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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$
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$\lim_{x\to1}\left(\frac{x^5-1}{\left(x-1\right)\left(x^2+x+1\right)}\right)$
Learn how to solve problems step by step online. Find the limit of (x^5-1)/(x^3-1) as x approaches 1. Factor the difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2). We can factor the polynomial x^5-1 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^5-1 will then be.
