Rationalize the Denominator of the Expression and Simplify $\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }$

question 38

Multiple Choice

Rationalize the denominator of the expression and simplify. $\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }$

• A) \(\frac { 2 x + 15 \sqrt { x } - 4 } { 4 x - 7 }\)
• B) \(\frac { 2 x - \sqrt { x } - 28 } { 4 x - 49 }\)
• C) \(\frac { x - \sqrt { x } - 28 } { 2 x - 49 }\)
• D) \(\frac { x + 15 \sqrt { x } - 4 } { 2 x - 7 }\)
• E) \(\frac { 2 x + 9 \sqrt { x } - 4 } { 4 x - 7 }\)

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Definitions:

Hydroxide

A negatively charged ion (OH-) consisting of oxygen and hydrogen.

Diazomethane

A highly reactive organic compound with the formula CH2N2, used in organic synthesis to introduce methyl groups or to form diazo compounds.

Carbene

A highly reactive molecule featuring a carbon atom with two non-bonded electrons and six valence electrons in total.

Carbanion

An ion that contains a negatively charged carbon atom, often a reactive intermediate in organic reactions.