Problem: When written with a rational denominator, the expression 2​+3​−5​2​​ is equivalent to:
Answer Choices:
A. 63+6​+15​​
B. 66​−2+10​​
C. 102+6​+10​​
D. 62+6​−10​​
E. none of these
Solution:
(2​+3​)−5​2​​⋅(2​+3​)+5​(2​+3​)+5​​=26​2+6​+10​​
26​2+6​+10​​⋅6​6​​=2⋅626​+6+215​​=63+6​+15​​