Answer:
[tex]\displaystyle \frac{4x + 14}{2} \div \frac{4x + 14}{x - 6} = \frac{x - 6}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Dividing Fractions - KCF (Keep Change Flip)
- Keep the 1st fraction the same
- Change the sign from division to multiplication
- Flip the 2nd fraction (reciprocate)
Algebra I
- Terms/Coefficients
- Domains
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{4x + 14}{2} \div \frac{4x + 14}{x - 6}[/tex]
Step 2: Simplify
- Divide [KCF]: [tex]\displaystyle \frac{4x + 14}{2} \cdot \frac{x - 6}{4x + 14}[/tex]
- Multiply: [tex]\displaystyle \frac{(4x + 14)(x - 6)}{2(4x + 14)}[/tex]
- Divide: [tex]\displaystyle \frac{(x - 6)}{2}[/tex]
Extra:
If we were to graph this, we would need to watch out for domain restrictions or changes because we are combining 2 domains together when 1 of them has a restriction.
