SOLUTION: simplify {{{ (1 + sqrt(3)) / (1 - sqrt(3)) }}}

Algebra ->  Square-cubic-other-roots -> SOLUTION: simplify {{{ (1 + sqrt(3)) / (1 - sqrt(3)) }}}      Log On


   

Question 674307: simplify +%281+%2B+sqrt%283%29%29+%2F+%281+-+sqrt%283%29%29+
Answer by jokaehler(26) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify.
+%281+%2B+sqrt%283%29%29+%2F+%281+-+sqrt%283%29%29+

We want to multiply the denominator by its conjugate in order to make the denominator equal "1." The denominator's conjugate is +%281+%2B+sqrt%283%29%29+. Now we have...

+%281+%2B+sqrt%283%29%29%281+%2B+sqrt%283%29%29+


Use the FOIL method to simplify.

+1+%2B+sqrt%283%29+%2B+sqrt%283%29+%2B+3+
Combine like terms.
+4+%2B+2sqrt%283%29+