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

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

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Answer 1 · 2016-08-01T13:09:59

$= 3 \frac{\sqrt{3} + 1}{2}$ $=3(sqrt3+1)/2$

Explanation:

Multiplying numerator and denominator of $\frac{3}{\sqrt{3} - 1}$ $3/(sqrt3-1)$ by $\sqrt{3} + 1$ $sqrt3+1$
we get
$3 \frac{\sqrt{3} + 1}{(\sqrt{3} - 1) (\sqrt{3} + 1)}$ $3(sqrt3+1)/((sqrt3-1)(sqrt3+1)$
$= 3 \frac{\sqrt{3} + 1}{3 - 1}$ $=3(sqrt3+1)/(3-1)$
$= 3 \frac{\sqrt{3} + 1}{2}$ $=3(sqrt3+1)/2$

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

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