Question

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Answer 1

Answer:

The value of the rational expression when x = -3 is undefined.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra II

Rational Functions

• Asymptotes, Holes

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \frac{x}{x^2 - 9} ,\ x = -3$

Step 2: Find Value

1. [Rational Expression] Substitute in x:
   $\displaystyle\begin{aligned}\frac{x}{x^2 - 9} ,\ x = -3 & \rightarrow \frac{-3}{(-3)^2 - 9} \\\end{aligned}$
2. [Order of Operations] Evaluate:
   $\displaystyle\begin{aligned}\frac{x}{x^2 - 9} ,\ x = -3 & \rightarrow \frac{-3}{(-3)^2 - 9} \\& \rightarrow \frac{-3}{0}\end{aligned}$

∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.

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Topic: Algebra II