Rationalizing the Denominator
If an expression such as
appears in a denominator,
we can multiply both the numerator and denominator by its conjugate
to get a rational number in the denominator.
Example 1
Rationalizing the denominator using conjugates
Write in simplified form.
Solution


Multiply the numerator and denominator by






Simplify. 


Multiply the numerator and
denominator by




Helpful hint
The expressions in Example 1
are the types of expressions
that you must simplify when
learning the quadratic formula.
