Summarize:

A fraction is written correctly when there is no radical in the denominator. If the denominator contains a square root or other radical, you must multiply both the top and bottom by a number that can get rid of that radical. Note that the numerator can contain a radical. Don't worry about the numerator. Failed to parse (syntax error): {\displaystyle
rac{7\sqrt{3}}{2\sqrt{7}} We can see that there is a 7{\displaystyle {\sqrt {7}}} in the denominator. A fraction with a monomial term in the denominator is the easiest to rationalize. Both the top and bottom of the fraction must be multiplied by the same term, because what you are really doing is multiplying by 1. 732777{\displaystyle {
rac {7{\sqrt {3}}}{2{\sqrt {7}}}}\cdot {
rac {\sqrt {7}}{\sqrt {7}}}}
Examine the fraction. Multiply the numerator and denominator by the radical in the denominator.