Question 78946
Problem:  Rationalize {{{5/(7-sqrt(14))}}}

Multiple the top and bottom by the conjugate of {{{7-sqrt(14)}}} which is {{{7+sqrt(14)}}}.

{{{5/(7-sqrt(14)) * (7+sqrt(14))/(7+sqrt(14))}}}

The numerator becomes {{{5(7+sqrt(14))=35+5sqrt(14)}}}
The denominator becomes {{{(7-sqrt(14))(7+sqrt(14))=49-14=35}}}

So the problem reduces to:

{{{(35+5sqrt(14))/35=1+sqrt(14)/7}}}.  So you are correct!

QED