** Final answer to the problem

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** Step-by-step Solution **

** How should I solve this problem?

- Choose an option
- 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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Simplifying

Learn how to solve limits by direct substitution problems step by step online.

$\lim_{x\to3}\left(\frac{x^2-8x+7}{x^3-3x+2}\right)$

Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x^2+1*-8x+7)/(x^3+1*-3x+2) as x approaches 3. Simplifying. We can factor the polynomial x^3-3x+2 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 2. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3-3x+2 will then be.

** Final answer to the problem

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