Rationalize the denominator and simplify. $$\frac { 5 } { \sqrt { 5 } + 1 }$$

Name: Rationalize the denominator and simplify. \[\frac { 5 } { \sqrt { 5 } + 1 }\]
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Quizplus · Accepted Answer

To rationalize the denominator of $\frac{5}{\sqrt{5} + 1}$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt{5} - 1$. This results in $\frac{5(\sqrt{5} - 1)}{(\sqrt{5} + 1)(\sqrt{5} - 1)} = \frac{5(\sqrt{5} - 1)}{5 - 1} = \frac{5(\sqrt{5} - 1)}{4}$, which matches choice A.

Rationalize the Denominator and Simplify 55+1\frac { 5 } { \sqrt { 5 } + 1 }5​+15​

Rationalize the Denominator and Simplify $\frac { 5 } { \sqrt { 5 } + 1 }$