Rationalize the denominator and simplify.

Name: Rationalize the denominator and simplify.
Brand: Quizplus
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Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of $\sqrt{9d^2e^2-c^2}$ is $\sqrt{9d^2e^2-c^2}$. Multiplying gives us:
$$\frac{11ec}{\sqrt{9d^2e^2-c^2}} \cdot \frac{\sqrt{9d^2e^2+c^2}}{\sqrt{9d^2e^2+c^2}} = \frac{11ec\sqrt{9d^2e^2+c^2}}{9d^2e^2-c^2}$$
So the answer is (B).

Rationalize the Denominator and Simplify