How do you rationalize the denominator and simplify $(2+sqrt3)/(2-sqrt3)$ ?

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Answer 1 · 2017-01-24T05:28:53

$7+4sqrt3$

Since

$(a-b)(a+b)=a^2-b^2$ ,

you would multiply both the terms of the fraction by

$2+sqrt3$ ,

then you get the expression:

$((2+sqrt3)color(red)((2+sqrt3)))/((2-sqrt3)color(red)((2+sqrt3)))$

that's

$(4+4sqrt3+3)/(4-3)=7+4sqrt3$

How do you rationalize the denominator and simplify (2+sqrt3)/(2-sqrt3)(2+sqrt3)/(2-sqrt3)?