Simplify by Rationalizing the Denominator $\frac { 3 \sqrt { x } + \sqrt { y } } { \sqrt { y } - 3 \sqrt { x } }$

question 16

Multiple Choice

Simplify by rationalizing the denominator.
- $\frac { 3 \sqrt { x } + \sqrt { y } } { \sqrt { y } - 3 \sqrt { x } }$

• A) \(\frac { 9 x + \sqrt { y } + 6 \sqrt { x y } } { y - 9 x }\)
• B) \(\frac { 9 x + y + 6 \sqrt { x y } } { y - 3 x }\)
• C) \(\frac { 9 \sqrt { x } + y + 6 \sqrt { x y } } { y - 9 x }\)
• D) \(\frac { 9 x + y + 6 \sqrt { x y } } { y - 9 x }\)

---

Definitions:

Subjectivity

Subjectivity refers to how someone's judgment is shaped by personal opinions and feelings instead of outside influences, making it inherently individual and biased.

Inner Judgment

The process of evaluating one's own thoughts, actions, and emotions based on personal standards and beliefs.

Biases

Prejudices or inclinations that can influence judgment or decision-making, often in an unfair or dismissive manner.

Subjective

Based on or influenced by personal feelings, tastes, or opinions, as opposed to objective observations or evidence.