Rationalize the denominator and simplify.
-$\frac{\sqrt{6}}{6 \sqrt{3}-\sqrt{6}}$
A) $\frac{3 \sqrt{2}+1}{17}$
B) $\frac{\sqrt{3}+1}{17}$
C) $\frac{3 \sqrt{2}-1}{17}$
D) $\frac{3 \sqrt{2}+1}{19}$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator, which is $6\sqrt{3} + \sqrt{6}$. This results in $\frac{\sqrt{6}(6\sqrt{3} + \sqrt{6})}{(6\sqrt{3} - \sqrt{6})(6\sqrt{3} + \sqrt{6})}$. Simplifying the denominator using the difference of squares formula gives $36*3 - 6$, which simplifies to $108 - 6 = 102$. Simplifying the numerator gives $6\sqrt{18} + 6$, which simplifies to $18\sqrt{2} + 6$. Dividing both numerator and denominator by 6 gives $\frac{3\sqrt{2} + 1}{17}$.

Rationalize the Denominator and Simplify 663−6\frac{\sqrt{6}}{6 \sqrt{3}-\sqrt{6}}63​−6​6​​ A) 32+117\frac{3 \sqrt{2}+1}{17}1732​+1​ B) 3+117\frac{\sqrt{3}+1}{17}173​+1​ C) 32−117\frac{3 \sqrt{2}-1}{17}1732​−1​

Rationalize the Denominator and Simplify $\frac{\sqrt{6}}{6 \sqrt{3}-\sqrt{6}}$ A) $\frac{3 \sqrt{2}+1}{17}$ B) $\frac{\sqrt{3}+1}{17}$ C) $\frac{3 \sqrt{2}-1}{17}$