Rationalize the denominator and simplify.
-$\frac { \sqrt { 5 } } { \sqrt { 3 } + 7 }$
A) $\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { - 46 }$
B) $\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { 10 }$
C) $\frac { 3 \sqrt { 15 } + 3 \sqrt { 5 } } { 21 }$
D) $\frac { \sqrt { 15 } + 7 \sqrt { 5 } } { - 46 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator, which is $\sqrt{3} - 7$. This results in $\frac{\sqrt{5}(\sqrt{3} - 7)}{(\sqrt{3} + 7)(\sqrt{3} - 7)} = \frac{\sqrt{15} - 7\sqrt{5}}{3 - 49} = \frac{\sqrt{15} - 7\sqrt{5}}{-46}$.

Rationalize the Denominator and Simplify 53+7\frac { \sqrt { 5 } } { \sqrt { 3 } + 7 }3​+75​​

Rationalize the Denominator and Simplify $\frac { \sqrt { 5 } } { \sqrt { 3 } + 7 }$