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
Solutions
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