How do you rationalize the denominator and simplify $1/(sqrta+sqrtb)$ ?

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Answer 1 · 2016-03-12T22:18:25

$=(sqrt(a)-sqrt(b))/(a-b)$

Given: $" "1/(sqrt(a)+sqrt(b))$

Known: $(a^2-b^2)=(a+b)(a-b)$

So using the above known information multiply by 1 but in the form of $1=(sqrt(a)-sqrt(b))/(sqrt(a)-sqrt(b))$

So
$=1/(sqrt(a)-sqrt(b)) xx (sqrt(a)-sqrt(b))/(sqrt(a)-sqrt(b))$

$=(sqrt(a)-sqrt(b))/(a-b)$

How do you rationalize the denominator and simplify 1/(sqrta+sqrtb)1/(sqrta+sqrtb)?