Learn how to solve problems step by step online. Find the limit of (x^3+2x^2-xx)/(x^3-7x+6) as x approaches 1. Cancel like terms -x and x. We can factor the polynomial x^3-7x+6 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 6. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3-7x+6 will then be.

Find the limit of (x^3+2x^2-xx)/(x^3-7x+6) as x approaches 1