How do you rationalize the denominator and simplify #(4 (sqrt3) + 2)/(2 (sqrt 3) + 1)#?
1 Answer
Apr 19, 2018
2
Explanation:
- 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))# - Re-format expression.
#((4\sqrt3+2)(2\sqrt3-1))/((2\sqrt3+1)(2\sqrt3-1))# - FOIL numerator and denominator
#(8(3)-4\sqrt3+4\sqrt3-2)/(4(3)-2\sqrt3+2\sqrt3-1)# - Simplify.
#(24-2)/(12-1)#
#22/11# - Simplify again:
#22/11=2#
