Question

Which choice is equivalent to the fraction below when xis an appropriate value? Hint: Rationalize the denominator and simplify. 3 3 - 6x OA 3+ Vox 9 - 2x B. 3 + 6x 3- 2x O c. 3 + √6x 9 - 6x O D. 3 + √6x 3-6x SUBMIT

Answer 1

The given expression can be rationalized as,

$\begin{gathered} =\frac{3}{3-\sqrt[]{6x}}\times\frac{3+\sqrt[]{6x}}{3+\sqrt[]{6x}} \\ =\frac{3(3+\sqrt[]{6x})}{3^2-(\sqrt[]{6x)^2}} \\ =\frac{3(3+\sqrt[]{6x})}{9-6x^{}} \\ =\frac{3(3+\sqrt[]{6x})}{3(3-2x)^{}} \\ =\frac{(3+\sqrt[]{6x})}{(3-2x)^{}} \end{gathered}$

Hence, optoion B is correct.