Answer:
[tex]=2(\sqrt[]{x}+\sqrt[]{x-6}_{})[/tex]
Step-by-step explanation:
To rationalize the term we multiply and divide the given expression by the reciprocal:
[tex]\frac{12}{\sqrt[]{x}-\sqrt[]{x-6}}\cdot\frac{\sqrt[]{x}+\sqrt[]{x-6}}{\sqrt[]{x}+\sqrt[]{x-6}}[/tex]
Solving:
[tex]\begin{gathered} \frac{12}{\sqrt[]{x}-\sqrt[]{x-6}}\cdot\frac{\sqrt[]{x}+\sqrt[]{x-6}}{\sqrt[]{x}+\sqrt[]{x-6}} \\ =\frac{12(\sqrt[]{x}+\sqrt[]{x-6})}{(\sqrt[]{x}-\sqrt[]{x-6})(\sqrt[]{x}+\sqrt[]{x-6})} \\ =\frac{12(\sqrt[]{x}+\sqrt[]{x-6})}{(\sqrt[]{x})^2-(\sqrt[]{x-6})^2} \\ =\frac{12(\sqrt[]{x}+\sqrt[]{x-6})}{x-x+6} \\ =2(\sqrt[]{x}+\sqrt[]{x-6}_{}) \end{gathered}[/tex]
