Question

Simplify the following expression.


`\displaystyle{(4x+14)/(2)/(4x+14)/(x-6)}`

Answer 1

(x-6)/2

Explanation:

Turn the second fraction upside down and multiply two fractions

Answer 2

`\displaystyle (4x + 14)/(2) / (4x + 14)/(x - 6) = (x - 6)/(2)`

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

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

Explanation:

Step 1: Define

`\displaystyle (4x + 14)/(2) / (4x + 14)/(x - 6)`

Step 2: Simplify

1. Divide [KCF]:
   `\displaystyle (4x + 14)/(2) \cdot (x - 6)/(4x + 14)`
2. Multiply:
   `\displaystyle ((4x + 14)(x - 6))/(2(4x + 14))`
3. Divide:
   `\displaystyle ((x - 6))/(2)`

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.