Rationalize the denominator. Assume all variables represent positive real numbers.
-$\frac { 2 } { 3 - \sqrt { 2 } }$
A) $\frac { 6 + 2 \sqrt { 2 } } { - 1 }$
B) $\frac { 2 } { 3 } - \frac { 2 } { \sqrt { 2 } }$
C) $\frac { 6 - 2 \sqrt { 2 } } { 7 }$
D) $\frac { 6 + 2 \sqrt { 2 } } { 7 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 2 } { 3 - \sqrt { 2 } }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $3 + \sqrt{2}$. This results in $\frac{2(3 + \sqrt{2})}{(3 - \sqrt{2})(3 + \sqrt{2})}$. Simplifying, the denominator becomes $3^2 - (\sqrt{2})^2 = 9 - 2 = 7$, and the numerator becomes $6 + 2\sqrt{2}$. Thus, the rationalized form is $\frac{6 + 2\sqrt{2}}{7}$.

Rationalize the Denominator 23−2\frac { 2 } { 3 - \sqrt { 2 } }3−2​2​

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