Question

how can you write 1 + √(3) ÷ 5 - √(3) with rationalized denominator

Answer 1

Hey, Dr. Jefferson, I strongly suggest that you enclose both numerator and denominator inside parentheses. otherwise your equation is subject to misinterpretation.
\[\frac{ 1+\sqrt{3} }{ 5-\sqrt{3} }\] is unacceptable because it has a radical in the denominator.

Answer 2

Have you heard of or used "conjugates" in your algebra course? If not, hope you'll look that term up. In this case, to get rid of the radical in the denominator, we multiply both numerator and denominator of your original expression by the CONJUGATE of 5-Sqrt(3). It's 5+Sqrt(3). Please try this.