Consider the given expression,
[tex]\frac{4}{\sqrt[]{x-2}-\sqrt[]{x}}[/tex]Rationalize the denominator asfollows,
[tex]\frac{4}{\sqrt[]{x-2}-\sqrt[]{x}}\times\frac{\sqrt[]{x-2}+\sqrt[]{x}}{\sqrt[]{x-2}+\sqrt[]{x}}=\frac{4(\sqrt[]{x-2}+\sqrt[]{x})}{(\sqrt[]{x-2})^2-(\sqrt[]{x})^2}=\frac{4(\sqrt[]{x-2}+\sqrt[]{x})}{x-2-x}=-2(\sqrt[]{x-2}+\sqrt[]{x})[/tex]The given option (c)
