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

1 Answer
Apr 19, 2018

Answer:

2

Explanation:

  1. 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))#
  2. Re-format expression.
    #((4\sqrt3+2)(2\sqrt3-1))/((2\sqrt3+1)(2\sqrt3-1))#
  3. FOIL numerator and denominator
    #(8(3)-4\sqrt3+4\sqrt3-2)/(4(3)-2\sqrt3+2\sqrt3-1)#
  4. Simplify.
    #(24-2)/(12-1)#
    #22/11#
  5. Simplify again:
    #22/11=2#