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#