Question

Simplify completely and find the restrictions on the variable.​

Answer 1

Answer:

$\displaystyle \frac{8}{x - 11}, x \neq 2, 11$

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

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{8x - 16}{x^2 - 13x + 22}$

Step 2: Simplify

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

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.