Simplify by rationalizing the denominator.
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Question

Quizplus · Accepted Answer

To rationalize the denominator of the given expression, we need to multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt{b}+\sqrt{a}$. This results in:
$$\frac{1}{\sqrt{b}-\sqrt{a}}\cdot\frac{\sqrt{b}+\sqrt{a}}{\sqrt{b}+\sqrt{a}}=\frac{\sqrt{b}+\sqrt{a}}{b-a}$$
Therefore, the simplified expression is $\frac{\sqrt{b}+\sqrt{a}}{b-a}$, which matches with choice C. To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator. In this case, the denominator is $\sqrt{b^2 - a^2}$, so the conjugate is $\sqrt{b^2 - a^2}$. Therefore, we need to multiply both the numerator and denominator by $\sqrt{b^2 - a^2}$: $$\frac{1}{\sqrt{b^2 - a^2}} \cdot \frac{\sqrt{b^2 - a^2}}{\sqrt{b^2 - a^2}} = \frac{\sqrt{b^2 - a^2}}{b^2 - a^2}.$$ Simplifying this expression gives us the answer in choice C.

Simplify by Rationalizing the Denominator