Question 1113566
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<pre>
  x = {{{(2+sqrt(3))/(2-sqrt(3))}}} = rationalize the fraction = {{{(2+sqrt(3))/(2-sqrt(3))}}} . {{{(2+sqrt(3))/(2+sqrt(3))}}}  = {{{(2+sqrt(3))^2/(2^2 - (sqrt(3))^2)}}}  =  {{{(4 + 4*sqrt(3) + 3)/(4-3)}}} = {{{7+4*sqrt(3)}}} .


Then  x + {{{1/x}}} = {{{7+4*sqrt(3)}}} + {{{1/(7+4*sqrt(3))}}} = rationalize the fraction = {{{7+4*sqrt(3)}}} + {{{1/(7+4*sqrt(3))}}} . {{{(7-4*sqrt(3))/(7-4*sqrt(3))}}} = 


= {{{7+4*sqrt(3)}}}  + {{{(7-4*sqrt(3))/(7^2 - (4*sqrt(3))^2)}}} = {{{7+4*sqrt(3)}}} + {{{(7-4*sqrt(3))/(49 - 48)}}} = {{{7+4*sqrt(3)}}} + {{{7-4*sqrt(3)}}} = 7 + 7 = 14.


<U>Answer</U>.  14.
</pre>

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On rationalizing fractions, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/HOW-TO-make-the-denominator-of-a-fraction-free-of-square-roots.lesson>HOW TO rationalize a fraction by making its denominator free of square roots</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/How-to-rationalize-a-fraction-by-making-its-denominator-free-of-cubic-roots.lesson>HOW TO rationalize a fraction by making its denominator free of cubic roots</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Amazing-calculations-with-fractions-that-contain-quadratic-irrationalities-in-denominators.lesson>Amazing calculations with fractions that contain quadratic irrationalities in denominators</A>

in this site.