Simplify by rationalizing the denominator.
-$\frac { \sqrt { x } - 20 } { \sqrt { x } + \sqrt { 6 } }$
A) $\frac { \sqrt { 6 x } + 20 \sqrt { x } - 20 \sqrt { 6 } } { 6 }$
B) $\frac { x - \sqrt { 6 x } - 20 \sqrt { x } + 20 \sqrt { 6 } } { x - 6 }$
C) $\frac { x - 26 \sqrt { x } + 20 \sqrt { 6 } } { x - 6 }$
D) $\frac { - 20 \sqrt { 6 } } { 6 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { \sqrt { x } - 20 } { \sqrt { x } + \sqrt { 6 } }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt { x } - \sqrt { 6 }$. This results in $\frac { (\sqrt { x } - 20)(\sqrt { x } - \sqrt { 6 }) } { (\sqrt { x } + \sqrt { 6 })(\sqrt { x } - \sqrt { 6 }) }$. Simplifying the numerator and denominator separately, the denominator becomes $x - 6$, and the numerator simplifies to $x - \sqrt { 6x } - 20\sqrt { x } + 20\sqrt { 6 }$, matching choice B.

Simplify by Rationalizing the Denominator x−20x+6\frac { \sqrt { x } - 20 } { \sqrt { x } + \sqrt { 6 } }x​+6​x​−20​

Simplify by Rationalizing the Denominator $\frac { \sqrt { x } - 20 } { \sqrt { x } + \sqrt { 6 } }$