How do you rationalize $\frac{3}{\sqrt{3} - 1}$ $3/(sqrt3 - 1)$ ?

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Answer 1 · 2015-05-07T12:21:34

Multiply the numerator and denominator by the reciprocal of the denominator

$\frac{3}{\sqrt{3} - 1}$ $3/(sqrt(3)-1)$

$= \frac{3}{\sqrt{3} - 1} \times \frac{\sqrt{3} + 1}{\sqrt{3} + 1}$ $=3/(sqrt(3)-1) xx (sqrt(3)+1)/(sqrt(3)+1)$

$= \frac{3 (\sqrt{3} + 1)}{3 - 1}$ $=(3(sqrt(3)+1))/(3-1)$

$= \frac{3}{2} (\sqrt{3} + 1)$ $= 3/2 (sqrt(3)+1)$

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