The trick is to multiply the fraction by 1 in the form of the conjugate of the denominator divided by itself.
If you have an expression of the form , then its conjugate is , and vice versa of course.
Here your denominator expression is , so the conjugate is , so you need to multiply your original fraction by 1 in the form of
Notice that multiplying a binomial times its conjugate is the reverse of factoring the difference of two squares -- so the result is the first term squared minus the second term squared. Just use FOIL on the numerator expressions:
The result is a fraction with a rational number in the denominator, hence the name of the process.
