Rationalize the denominator. Give your answer in simplified form.

Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to eliminate any square root from the denominator. We can do this by multiplying both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of the denominator is $\sqrt{3}+\sqrt{5}$.

So, we have:

$$\frac{1}{\sqrt{3}-\sqrt{5}}=\frac{1}{\sqrt{3}-\sqrt{5}}\cdot\frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}+\sqrt{5}}=\frac{\sqrt{3}+\sqrt{5}}{3-5}=-\frac{\sqrt{3}+\sqrt{5}}{2}$$

Simplifying the expression, we get:

$$-\frac{\sqrt{3}+\sqrt{5}}{2}=-\frac{\sqrt{3}}{2}-\frac{\sqrt{5}}{2}$$

Therefore, the answer is B.

Rationalize the Denominator