Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero.
-$\frac{\sqrt{x}-\sqrt{y}}{\sqrt{6 x}+\sqrt{7 y}}$

A) $\frac{x \sqrt{6}-\sqrt{7 x y}-\sqrt{6 x y}+y \sqrt{7}}{6 x-7 y}$

B) $\frac{x \sqrt{6}-\sqrt{7 x y}-\sqrt{6 x y}+y \sqrt{7}}{6 x+7 y}$

C) $\frac{\sqrt{6 x}-\sqrt{13 x y}+\sqrt{7 y}}{6 x+7 y}$

D) $\frac{\sqrt{6 x}-\sqrt{13 x y}+\sqrt{7 y}}{6 x-7 y}$

Question

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero.
-$\frac{\sqrt{x}-\sqrt{y}}{\sqrt{6 x}+\sqrt{7 y}}$

A) $\frac{x \sqrt{6}-\sqrt{7 x y}-\sqrt{6 x y}+y \sqrt{7}}{6 x-7 y}$

B) $\frac{x \sqrt{6}-\sqrt{7 x y}-\sqrt{6 x y}+y \sqrt{7}}{6 x+7 y}$

C) $\frac{\sqrt{6 x}-\sqrt{13 x y}+\sqrt{7 y}}{6 x+7 y}$

D) $\frac{\sqrt{6 x}-\sqrt{13 x y}+\sqrt{7 y}}{6 x-7 y}$

Quizplus · Accepted Answer

To rationalize the denominator $\frac{\sqrt{x}-\sqrt{y}}{\sqrt{6 x}+\sqrt{7 y}}$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt{6 x}-\sqrt{7 y}$. This process eliminates the square roots in the denominator and simplifies to option A.

Rationalize the Denominator x−y6x+7y\frac{\sqrt{x}-\sqrt{y}}{\sqrt{6 x}+\sqrt{7 y}}6x​+7y​x​−y​​ A) x6−7xy−6xy+y76x−7y\frac{x \sqrt{6}-\sqrt{7 x y}-\sqrt{6 x y}+y \sqrt{7}}{6 x-7 y}6x−7yx6​−7xy​−6xy​+y7​​

Rationalize the Denominator $\frac{\sqrt{x}-\sqrt{y}}{\sqrt{6 x}+\sqrt{7 y}}$ A) $\frac{x \sqrt{6}-\sqrt{7 x y}-\sqrt{6 x y}+y \sqrt{7}}{6 x-7 y}$