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

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