Rationalize the denominator and simplify.
-$\frac{3 \sqrt{3}+\sqrt{11}}{5 \sqrt{3}+\sqrt{13}}$

A) $\frac{45+2 \sqrt{6}-\sqrt{143}}{62}$

B) $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{88}$

C) $\frac{45+5 \sqrt{33}+3 \sqrt{39}+\sqrt{143}}{62}$

D) $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{62}$

Question

Rationalize the denominator and simplify.
-$\frac{3 \sqrt{3}+\sqrt{11}}{5 \sqrt{3}+\sqrt{13}}$

A) $\frac{45+2 \sqrt{6}-\sqrt{143}}{62}$

B) $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{88}$

C) $\frac{45+5 \sqrt{33}+3 \sqrt{39}+\sqrt{143}}{62}$

D) $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{62}$

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, $5 \sqrt{3} - \sqrt{13}$. Simplifying gives the expression in choice D.