Learn how to solve problems step by step online. Find the limit of (x^3-6x^29x)/(x^3+5x^23x+-9) as x approaches -3. We can factor the polynomial x^3+5x^2+3x-9 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 -9. 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+5x^2+3x-9 will then be. Trying all possible roots, we found that -3 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.

Find the limit of (x^3-6x^29x)/(x^3+5x^23x+-9) as x approaches -3