To simplify the expression \(\frac{x - 5}{x^3 - 2x^2 - 11x - 20}\), we can start by factoring the cubic polynomial in the denominator, if possible.

### Step 1: Factor the denominator
We are looking to factor:
\[
x^3 - 2x^2 - 11x - 20
\]
Using the Rational Root Theorem, we test possible rational roots such as \( \pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20 \).

Let's start by checking \(x = -4\):

\[
(-4)^3 - 2(-4)^2 - 11(-4) - 20 = -64 - 32 + 44 - 20 = -72
\]
This is not zero, so \(x = -4\) is not a root.

Now, let's check \(x = -2\):

\[
(-2)^3 - 2(-2)^2 - 11(-2) - 20 = -8 - 8 + 22 - 20 = -14
\]
So \(x = -2\) is not a root.

We will divide the polynomial

Learn how to simplify the rational expression (x - 5) / (x^3 - 2x^2 - 11x - 20) by factoring the cubic polynomial in the denominator and applying polynomial division. This problem involves key algebraic concepts such as factoring, the Rational Root Theorem, and polynomial simplification, suitable for students in Grades 10-12.

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