Question

Which choice is equivalent to the fraction below when x2 1? Hint: Rationalize the denominator and simplify. 1 √x - √x-1 O A. - x - 1 - fx O B. x B. + VX-1 o + - 2x-1 O D. &x - √x-1

Answer 1

We have

`\frac{\sqrt[]{8}}{\sqrt[]{2}-2}`
`\frac{\sqrt[]{4\cdot2}}{\sqrt[]{2}-2}`
`\frac{\sqrt[]{4}\cdot\sqrt[]{2}}{\sqrt[]{2}-2}`
`\frac{2\sqrt[]{2}}{\sqrt[]{2}-2}`

We rationalize the denominator

`\frac{\sqrt[]{2}+2}{\sqrt[]{2}+2}\cdot\frac{2\sqrt[]{2}}{\sqrt[]{2}-2}`

then we simplify

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

Finally, we obtain

`-2-2\sqrt[]{2}`