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 Question from Agnes, a student: simplify (1-√3)(1÷3+√3)

HI Agnes,

You have written the expression

$\left( 1 + \sqrt{3}\right) \left( \frac13 + \sqrt{3}\right)$

but I think what the expression should be is

$\left( 1 + \sqrt{3}\right) \left( \frac{1}{3 + \sqrt{3}}\right)= \frac{1 + \sqrt{3}}{3 + \sqrt{3}}.$

If I am correct then you need to "rationalize the denominator" by multiplying the numerator and denominator by

$3 - \sqrt{3}.$

I hope this helps,
Penny

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