Rationalize the denominator: $\frac { 6 } { 2 \sqrt { 3 } - 1 }$
A) $\frac { 12 \sqrt { 3 } + 6 } { 11 }$
B) $\frac { 12 \sqrt { 3 } + 1 } { 11 }$
C) $\frac { 12 \sqrt { 3 } + 6 } { 17 }$
D) none of these

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 6 } { 2 \sqrt { 3 } - 1 }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $2\sqrt{3} + 1$. This gives: $\frac{6(2\sqrt{3} + 1)}{(2\sqrt{3} - 1)(2\sqrt{3} + 1)} = \frac{12\sqrt{3} + 6}{(4*3) - 1} = \frac{12\sqrt{3} + 6}{12 - 1} = \frac{12\sqrt{3} + 6}{11}$.

Rationalize the Denominator 623−1\frac { 6 } { 2 \sqrt { 3 } - 1 }23​−16​

Rationalize the Denominator $\frac { 6 } { 2 \sqrt { 3 } - 1 }$