How do you rationalize the denominator and simplify $3/(2-sqrt5)$ ?

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Answer 1 · 2017-06-19T20:22:45

When given a fraction of the form:

$c/(a-sqrt(b)$

You rationalize the denominator by multiplying by 1 in the form $(a+sqrtb)/(a+sqrtb)$

Multiply the fraction by 1 in the form $(2+sqrt5)/(2+sqrt5)$ :

$3/(2-sqrt5)(2+sqrt5)/(2+sqrt5)$

$(3(2+sqrt5))/(2^2-(sqrt5)^2)$

$(3(2+sqrt5))/(4-5)$

$-3(2+sqrt5)$

$-6-3sqrt5$

How do you rationalize the denominator and simplify 3/(2-sqrt5)3/(2-sqrt5)?