Rationalize the denominator. $\frac { \sqrt { 7 } } { \sqrt { 5 } + 3 }$
A) $- \frac { 3 \sqrt { 7 } - \sqrt { 35 } } { 4 }$
B) $\frac { 3 \sqrt { 35 } - \sqrt { 7 } } { 4 }$
C) $\frac { 3 \sqrt { 7 } - \sqrt { 35 } } { 4 }$
D) $\frac { 3 \sqrt { 7 } + \sqrt { 35 } } { 4 }$
E) $- \frac { 3 \sqrt { 7 } + \sqrt { 35 } } { 4 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator, $\sqrt{5} - 3$. This results in $\frac{\sqrt{7}(\sqrt{5} - 3)}{(\sqrt{5} + 3)(\sqrt{5} - 3)}$. The denominator becomes $5 - 9 = -4$, and the numerator becomes $\sqrt{35} - 3\sqrt{7}$, leading to the expression $\frac{3\sqrt{7} - \sqrt{35}}{4}$.

Rationalize the Denominator 75+3\frac { \sqrt { 7 } } { \sqrt { 5 } + 3 }5​+37​​

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