Simplify by rationalizing the denominator.
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C) -1

Question

Quizplus · Accepted Answer

To simplify by rationalizing the denominator, we multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of $\sqrt{11ebb63d\_1c00\_1654\_b851\_273d91fca1e9}$ is $\sqrt{11ebb63d\_1c00\_1654\_b851\_273d91fca1e9}$. By multiplying both the numerator and denominator by this, we get:
$$\frac{1}{\sqrt{11ebb63d\_1c00\_1654\_b851\_273d91fca1e9}} \cdot \frac{\sqrt{11ebb63d\_1c00\_1654\_b851\_273d91fca1e9}}{\sqrt{11ebb63d\_1c00\_1654\_b851\_273d91fca1e9}} = \frac{\sqrt{11ebb63d\_1c00\_1654\_b851\_273d91fca1e9}}{(11ebb63d\_1c00\_1654\_b851\_273d91fca1e9)}.$$
Thus, the answer is B. To rationalize the denominator, we need to eliminate the square root. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is $\sqrt{2}+3$. Therefore,

$\frac{5}{\sqrt{2}-3}=\frac{5(\sqrt{2}+3)}{(\sqrt{2}-3)(\sqrt{2}+3)}=\frac{5\sqrt{2}+15}{2-9}=-\frac{5\sqrt{2}+15}{7}$

So, the answer is B.

Simplify by Rationalizing the Denominator