We are tasked with solving the inequality:

\[
\frac{x - 2}{x^2 - 3x - 10} \geq 0
\]

### Step 1: Factor the denominator
We begin by factoring the quadratic expression in the denominator:

\[
x^2 - 3x - 10 = (x - 5)(x + 2)
\]

Thus, the inequality becomes:

\[
\frac{x - 2}{(x - 5)(x + 2)} \geq 0
\]

### Step 2: Identify critical points
The critical points occur where the numerator or the denominator is zero. These points are:
- \(x - 2 = 0 \Rightarrow x = 2\)
- \(x

Learn how to solve the inequality (x - 2) / (x^2 - 3x - 10) ≥ 0 with a detailed step-by-step solution. This problem includes factoring quadratic expressions, identifying critical points, and performing sign analysis. Suitable for students in Grades 9-11.

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