Rationalize the Denominator and Simplify $\frac { 6 \sqrt { 2 } + \sqrt { 6 } } { 3 \sqrt { 2 } - \sqrt { 6 } }$

question 165

Multiple Choice

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
- $\frac { 6 \sqrt { 2 } + \sqrt { 6 } } { 3 \sqrt { 2 } - \sqrt { 6 } }$

• A) \(\frac { 7 + 3 \sqrt { 3 } } { 2 }\)
• B) \(\frac { 42 + 9 \sqrt { 12 } } { 12 }\)
• C) \(\frac { 42 + 18 \sqrt { 3 } } { 12 }\)
• D) \(\frac { 21 + 9 \sqrt { 3 } } { 6 }\)

---

Definitions:

First Stage

The initial phase or beginning of a process, event, or development.

Childbirth

The process of delivering a baby from the mother's uterus to the outside world.

Labor

The physical and mental efforts employed in economic production or service activities, often referring to both the workforce and the process of childbirth.

Mercury

A chemical element with the symbol Hg and atomic number 80, known for being a liquid metal at room temperature.