Rationalize the denominator and simplify.
-$\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }$
A) $\frac { 1 } { 13 } ( \sqrt { 14 } + 1 )$
B) $\frac { 1 } { 13 } ( \sqrt { 2 } + 1 )$
C) $\frac { 1 } { 15 } ( \sqrt { 14 } + 1 )$
D) $\frac { 1 } { 13 } ( \sqrt { 14 } - 1 )$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator, $7\sqrt{2} + \sqrt{7}$. This results in $\frac{\sqrt{7}(7\sqrt{2} + \sqrt{7})}{(7\sqrt{2} - \sqrt{7})(7\sqrt{2} + \sqrt{7})}$, which simplifies to $\frac{7\sqrt{14} + 7}{98 - 7}$ or $\frac{\sqrt{14} + 1}{13}$, matching choice A.

Rationalize the Denominator and Simplify 772−7\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }72​−7​7​​

Rationalize the Denominator and Simplify $\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }$