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) $\frac { - 12 + 3 \sqrt { x } } { x - 16 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate $\sqrt{x} - 4$. This results in $\frac{3(\sqrt{x} - 4)}{(\sqrt{x} + 4)(\sqrt{x} - 4)} = \frac{3\sqrt{x} - 12}{x - 16}$.

Rationalize the Denominator and Simplify 3x+4\frac { 3 } { \sqrt { x } + 4 }x​+43​

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