Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 446: 97

Rationalizing the denominator does not change the value of the original expression because multiplying both the numerator and the denominator by the same number is equivalent to multiplying the expression by $1.$

Any number/expression multiplied by $1$ is equal to the number/expression itself. The value does not change - only the form of the original expression changes.