= 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,
$$
\frac1{\sqrt a+b}=\frac{\sqrt a-b}{a-b^2}
$$
when $a\geq0$ 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.
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