Question

Simplify completely and find the restrictions on the variable.​

Answer 1

`\displaystyle (8)/(x - 11), x \\eq 2, 11`

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 (8x - 16)/(x^2 - 13x + 22)`

Step 2: Simplify

1. [Fraction] Factor numerator:
   `\displaystyle (8(x - 2))/(x^2 - 13x + 22)`
2. [Fraction] Factor denominator:
   `\displaystyle (8(x - 2))/((x - 11)(x - 2))`
3. [Fraction] Divide:
   `\displaystyle (8)/(x - 11)`

We know that x cannot equal 11, because that would give us a divide by 0 error and we know that x cannot equal 2 because it was canceled out when simplifying.