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Precalculus: Rationalizing expressions



1. Recall the following remarkable identities:

(a + b)2 = a2 + 2ab + b2

(a - b)2 = a2 - 2ab + b2

(a + b)(a - b) = a2 - b2

To rationalize an expression means eliminating the square roots from the denominator or from the numerator of this expression.

To do this we use the third identity:

a2 - b2 = (a + b)(a - b)

2. Worked Example:

1/(√a + √b) = (√a - √b)/(√a + √b)(√a -√b) =
(√a - √b)/(a2 - b2)



3. Exercises:

Rationalize the following expressions:

2(a + b)/(√a + √b)

(√a - √b)/2(a + b)

(n2 + 7n)1/2 - n


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