How do you rationalize the denominator and simplify $(4 (sqrt3) + 2)/(2 (sqrt 3) + 1)$ ?

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Answer 1 · 2018-04-19T21:27:25

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Multiply by the conjugate (see here) of the denominator, $2(\sqrt3)-1$ .
$(4 (sqrt3) + 2)/(2 (sqrt 3) + 1)xx\color(crimson)((2\sqrt3-1)/(2\sqrt3-1))$
Re-format expression.
$((4\sqrt3+2)(2\sqrt3-1))/((2\sqrt3+1)(2\sqrt3-1))$
FOIL numerator and denominator
$(8(3)-4\sqrt3+4\sqrt3-2)/(4(3)-2\sqrt3+2\sqrt3-1)$
Simplify.
$(24-2)/(12-1)$
$22/11$
Simplify again:
$22/11=2$

How do you rationalize the denominator and simplify (4 (sqrt3) + 2)/(2 (sqrt 3) + 1)(4 (sqrt3) + 2)/(2 (sqrt 3) + 1)?