Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$\frac { \sqrt { x } - 4 \sqrt { y } } { 2 \sqrt { x } }$
A) $\frac { x - 4 y } { 2 x + 8 \sqrt { x y } }$
B) $\frac { x - 16 y } { 2 x + 8 \sqrt { x y } }$
C) $\frac { x + 16 y } { 2 x - 8 \sqrt { x y } }$
D) $\frac { x - 16 y } { 2 x - 8 \sqrt { x y } }$

Question

Quizplus · Accepted Answer

To rationalize the numerator, multiply both the numerator and the denominator by the conjugate of the numerator, which is $\sqrt{x} + 4\sqrt{y}$. This results in $\frac{(\sqrt{x} - 4\sqrt{y})(\sqrt{x} + 4\sqrt{y})}{2\sqrt{x}(\sqrt{x} + 4\sqrt{y})}$. Simplifying the numerator using the difference of squares formula gives $x - 16y$, and the denominator simplifies to $2x + 8\sqrt{xy}$, resulting in $\frac{x - 16y}{2x + 8\sqrt{xy}}$.

Rationalize the Numerator and Simplify x−4y2x\frac { \sqrt { x } - 4 \sqrt { y } } { 2 \sqrt { x } }2x​x​−4y​​

Rationalize the Numerator and Simplify $\frac { \sqrt { x } - 4 \sqrt { y } } { 2 \sqrt { x } }$