The function ℎ(𝑥)=𝑥2−𝑥−2𝑥2−𝑥−6h(x)= x 2 −x−6x 2 −x−2​   has a vertical asymptote at x =A.- 2B.6C.3D.- 2 and 3E.- 1 and 2SUBMITarrow_backPREVIOUS

To find the vertical asymptote of the function $h(x) = \frac{x^2 - x - 6}{x^2 - x - 2}$, we need to identify the values of $x$ that make the denominator equal to zero.

Steps to Solve the Problem

1. Break Down the Problem

   • Identify the function's denominator: $x^2 - x - 2$.
   • Set the denominator equal to zero to find the vertical asymptotes.

2. Relevant Concepts

   • A vertical asymptote occurs where the function is undefined, which happens when the denominator is zero.

3. Analysis and Detail

   • Solve the equation: $x^2 - x - 2 = 0$
   • Factor the quadratic: $(x - 2)(x + 1) = 0$
   • Set each factor to zero:
     • $x - 2 = 0$ ⟹ $x = 2$
     • $x + 1 = 0$ ⟹ $x = -1$

4. Verify and Summarize

   • The values $x = 2$ and $x = -1$ are where the function $h(x)$ has vertical asymptotes.
   • Thus, the vertical asymptotes are at $x = -1$ and $x = 2$.

Final Answer

The correct answer is E. -1 and 2.