Question

Which choice is equivalent to the fraction below when x2 2? Hint: Rationalize the denominator and simplify. 4 O A. -2(&x-fx-2) O B. 2(x + √x-2) C. -2(x + x - 2) O D. 2(x - x - 2)

Answer 1

Consider the given expression,

`\frac{4}{\sqrt[]{x-2}-\sqrt[]{x}}`

Rationalize the denominator asfollows,

`\frac{4}{\sqrt[]{x-2}-\sqrt[]{x}}*\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})`

The given option (c)