Rationalize Denominators
-$\frac { 3 } { 4 - \sqrt { 2 } }$
A) $\frac { 12 + 3 \sqrt { 2 } } { 14 }$
B) $\frac { 12 - 3 \sqrt { 2 } } { 14 }$
C) $\frac { 12 + 3 \sqrt { 2 } } { 2 }$
D) $\frac { 3 } { 4 } - \frac { 3 } { \sqrt { 2 } }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 3 } { 4 - \sqrt { 2 } }$, multiply both the numerator and denominator by the conjugate of the denominator, which is $4 + \sqrt{2}$. This results in $\frac { 3(4 + \sqrt { 2 }) } { (4 - \sqrt { 2 })(4 + \sqrt { 2 }) }$, simplifying to $\frac { 12 + 3\sqrt { 2 } } { 16 - 2 }$ or $\frac { 12 + 3\sqrt { 2 } } { 14 }$.

Rationalize Denominators - 34−2\frac { 3 } { 4 - \sqrt { 2 } }4−2​3​

Rationalize Denominators
- $\frac { 3 } { 4 - \sqrt { 2 } }$