Rationalize the denominator. Assume that all variables represent positive numbers.
-$\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }$
A) $- 8 \sqrt { x }$
B) $\frac { x + 16 } { x - 16 }$
C) $\frac { x - 8 \sqrt { x } + 16 } { x - 16 }$
D) $- 1$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt { x } - 4$. This results in $\frac { (\sqrt { x } - 4)(\sqrt { x } - 4) } { (\sqrt { x } + 4)(\sqrt { x } - 4) }$. Simplifying this expression gives $\frac { x - 8 \sqrt { x } + 16 } { x - 16 }$, which matches choice C.

Rationalize the Denominator x−4x+4\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }x​+4x​−4​

Rationalize the Denominator $\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }$