Rationalize the denominator and simplify.
-$\frac { 5 } { 7 - \sqrt { 5 } }$
A) $\frac { 35 + 5 \sqrt { 5 } } { - 2 }$
B) $\frac { 35 + 5 \sqrt { 5 } } { 44 }$
C) $\frac { 35 - 5 \sqrt { 5 } } { 44 }$
D) $\frac { 5 } { 7 } - \frac { 5 } { \sqrt { 5 } }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 5 } { 7 - \sqrt { 5 } }$, multiply both the numerator and the denominator by the conjugate of the denominator, $7 + \sqrt{5}$. This results in $\frac{5(7 + \sqrt{5})}{(7 - \sqrt{5})(7 + \sqrt{5})}$, which simplifies to $\frac{35 + 5\sqrt{5}}{49 - 5}$ or $\frac{35 + 5\sqrt{5}}{44}$.

Rationalize the Denominator and Simplify 57−5\frac { 5 } { 7 - \sqrt { 5 } }7−5​5​

Rationalize the Denominator and Simplify $\frac { 5 } { 7 - \sqrt { 5 } }$