Rationalize the denominator and simplify.
-$\frac { 9 \sqrt { 3 } + \sqrt { 11 } } { 7 \sqrt { 3 } + \sqrt { 13 } }$
A) $\frac { 189 + 7 \sqrt { 33 } - 9 \sqrt { 39 } - \sqrt { 143 } } { 134 }$
B) $\frac { 189 - 2 \sqrt { 6 } - \sqrt { 143 } } { 134 }$
C) $\frac { 189 + 7 \sqrt { 33 } + 9 \sqrt { 39 } + \sqrt { 143 } } { 134 }$
D) $\frac { 189 + 7 \sqrt { 33 } - 9 \sqrt { 39 } - \sqrt { 143 } } { 160 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator, which is $7\sqrt{3} - \sqrt{13}$. The denominator becomes $7\sqrt{3} + \sqrt{13}$ times $7\sqrt{3} - \sqrt{13}$ = $49*3 - 13$ = $147 - 13$ = $134$. The numerator, when expanded, gives $189 + 7\sqrt{33} - 9\sqrt{39} - \sqrt{143}$.

Rationalize the Denominator and Simplify 93+1173+13\frac { 9 \sqrt { 3 } + \sqrt { 11 } } { 7 \sqrt { 3 } + \sqrt { 13 } }73​+13​93​+11​​

Rationalize the Denominator and Simplify $\frac { 9 \sqrt { 3 } + \sqrt { 11 } } { 7 \sqrt { 3 } + \sqrt { 13 } }$