Rationalize the Denominator $\frac { \sqrt { x } - \sqrt { y } } { \sqrt { 2 x } + \sqrt { 3 y } }$

question 290

Multiple Choice

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
- $\frac { \sqrt { x } - \sqrt { y } } { \sqrt { 2 x } + \sqrt { 3 y } }$

• A) \(\frac { x \sqrt { 2 } - \sqrt { 3 x y } - \sqrt { 2 x y } + y \sqrt { 3 } } { 2 x - 3 y }\)
• B) \(\frac { \sqrt { 2 x } - \sqrt { 5 x y } + \sqrt { 3 y } } { 2 x + 3 y }\)
• C) \(\frac { x \sqrt { 2 } - \sqrt { 3 x y } - \sqrt { 2 x y } + y \sqrt { 3 } } { 2 x + 3 y }\)
• D) \(\frac { \sqrt { 2 x } - \sqrt { 5 x y } + \sqrt { 3 y } } { 2 x - 3 y }\)

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Definitions:

Simple Interest

Interest computed solely on the initial amount invested, excluding any previously earned interest.

Investment

The undertaking of investing resources, usually capital, with the foresight of amassing income or profits.

Months

Units of time, typically used to measure periods within a year, consisting of 28 to 31 days.

Invested

Assigning monetary assets with the prospect of gaining returns or profit.