Question

Simplify completely and find the restrictions on the variable.​

Answer 1

`\displaystyle (x + 2)/(x + 9), \ x \\eq -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

Explanation:

Step 1: Define

`\displaystyle (x^2 - 10x - 24)/(x^2 - 3x - 108)`

Step 2: Simplify

1. [Fraction] Factor numerator:
   `\displaystyle ((x - 12)(x + 2))/(x^2 - 3x - 108)`
2. [Fraction] Factor denominator:
   `\displaystyle ((x - 12)(x + 2))/((x - 12)(x + 9))`
3. [Fraction] Divide:
   `\displaystyle (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.