Rationalizing a denominator

Multiplying numerator and denominator of a fraction by the same nonzero expression can remove a square root from the denominator. For instance,when $a\ge 0$ and both denominators are nonzero. This uses the difference-of-squares identity $(\sqrt{a}+b)(\sqrt{a}-b)=a-b^2$. If $a=b^2$, the original expression may still be defined even though the rationalized quotient is not, so that case must be handled separately. The related rationalization of a square-root difference applies the same multiplication to a numerator.