How do you simplify $(3+6sqrt3) / (5 + 12sqrt3)$ ?

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Answer 1 · 2017-01-18T22:55:34

$"3 + 6√3"/"5 + 12√3" = "(201 + 6√3)"/"407"$

$"3 + 6√3"/"5 + 12√3"$

Rationalising the denominator

$"3 + 6√3"/"5 + 12√3" × "5 - 12√3"/"5 - 12√3"$

$"(3 + 6√3)(5 - 12√3)"/"(5 + 12√3)(5 - 12√3)"$

$"(3)(5) - (3)(12√3) + (6√3)(5) - (6√3)(12√3)"/((5)^2 - (12√3)^2$

$"15 - 36√3 + 30√3 - 216"/"25 - 432"$

$"-201 - 6√3"/"-407"$

$"-(201 + 6√3)"/"-407"$

$"(201 + 6√3)"/"407"$

How do you simplify (3+6sqrt3) / (5 + 12sqrt3)(3+6sqrt3) / (5 + 12sqrt3)?