Rationalize the Denominator and Simplify $\frac { 3 } { \sqrt { x } + 4 }$

question 61

Multiple Choice

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
- $\frac { 3 } { \sqrt { x } + 4 }$

• A) \(\frac { - 12 - 3 \sqrt { x } } { x + 16 }\)
• B) \(\frac { - 12 + 3 \sqrt { x } } { x ^ { 2 } - 16 }\)
• C) \(\frac { - 12 - 3 \sqrt { x } } { x - 16 }\)
• D) \(\frac { - 12 + 3 \sqrt { x } } { x - 16 }\)

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Definitions:

Countertransference

The emotional reaction of a psychotherapist to a client's transference, including feelings, thoughts, or behaviors that emerge from the therapist's unconscious or personal experiences.

Transference

A psychoanalytic concept where feelings, desires, and expectations of one person are redirected and applied to another person, often in a therapeutic setting.

Unconscious Material

Content of the mind that is outside of conscious awareness, including desires, thoughts, and memories, which can influence behavior and perceptions.

Ego

In psychoanalysis, it represents the part of the personality that mediates between the conscious and unconscious aspects of oneself and is responsible for reality testing and a sense of personal identity.