Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$$\frac { \sqrt { 7 } + 5 } { \sqrt { 3 } }$$
A) $\frac { - 18 } { \sqrt { 21 } + 5 \sqrt { 3 } }$
B) $\frac { - 18 } { \sqrt { 21 } - 5 \sqrt { 3 } }$
C) $\frac { 35 } { 3 \sqrt { 21 } + 7 \sqrt { 3 } }$
D) $\frac { 12 } { \sqrt { 21 } - 5 \sqrt { 3 } }$

Question

Quizplus · Accepted Answer

Multiply the numerator and denominator by $\sqrt { 3 }$ to rationalize the numerator.$$\frac { \sqrt { 7 } + 5 } { \sqrt { 3 } } = \frac { \sqrt { 7 } + 5 } { \sqrt { 3 } } \cdot \frac { \sqrt { 3 } } { \sqrt { 3 } } = \frac { \sqrt { 21 } + 5 \sqrt { 3 } } { 3 }$$Simplify the numerator by combining like terms.$$\frac { \sqrt { 21 } + 5 \sqrt { 3 } } { 3 } = \frac { - 18 } { \sqrt { 21 } - 5 \sqrt { 3 } }$$

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

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