Question

Simplify completely and find the restrictions on the variable.​

Answer 1

Answer:

$\displaystyle \frac{x + 2}{x + 9}, \ x \neq -9, \ 12$

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 I

• Terms/Coefficients
• Factoring

Algebra II

• Discontinuities
• Domain Restrictions

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{x^2 - 10x - 24}{x^2 - 3x - 108}$

Step 2: Simplify

1. [Fraction] Factor numerator:                                                                           $\displaystyle \frac{(x - 12)(x + 2)}{x^2 - 3x - 108}$
2. [Fraction] Factor denominator:                                                                       $\displaystyle \frac{(x - 12)(x + 2)}{(x - 12)(x + 9)}$
3. [Fraction] Divide:                                                                                              $\displaystyle \frac{x + 2}{x + 9}$

We know that x cannot equal -9 because we would get a divide by 0 (undefined) error. We also know that x cannot equal 12 because it was canceled out when simplifying.