SOLUTION: Write in simplified radical form by rationalizing the denominator. {{{(2sqrt(3)+4)/(-2sqrt(3)+5)}}} is the answer (-32-18sqrt(3))/(-13)

Algebra ->  Radicals -> SOLUTION: Write in simplified radical form by rationalizing the denominator. {{{(2sqrt(3)+4)/(-2sqrt(3)+5)}}} is the answer (-32-18sqrt(3))/(-13)      Log On


   

Question 317291: Write in simplified radical form by rationalizing the denominator.
%282sqrt%283%29%2B4%29%2F%28-2sqrt%283%29%2B5%29
is the answer
(-32-18sqrt(3))/(-13)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%282sqrt%283%29%2B4%29%2F%28-2sqrt%283%29%2B5%29

Put parentheses around the numeratior and denominator:

%28%282sqrt%283%29%2B4%29%29%2F%28%28-2sqrt%283%29%2B5%29%29

Form the conjugate of the denominator by changing the
sign of the second term, that is, %28-2sqrt%283%29-5%29, put it over
itself, %28%28-2sqrt%283%29-5%29%29%2F%28%28-2sqrt%283%29-5%29%29, which has value 1.
So we may multiply it by the original without changing the value

%28%282sqrt%283%29%2B4%29%29%2F%28%28-2sqrt%283%29%2B5%29%29%22%D7%22%28%28-2sqrt%283%29-5%29%29%2F%28%28-2sqrt%283%29-5%29%29%22=%22%22=%22%22=%22-12-18sqrt%283%29-20%29%2F%2812-25%29%22=%22%28-32-18sqrt%283%29%29%2F%28-13%29

That's what you got but you can simplify it by multiplying by %28-1%29%2F%28-1%29

%28-1%29%2F%28-1%29%22%D7%22%28%28-32-18sqrt%283%29%29%29%2F%28%28-13%29%29%22=%22%2832%2B18sqrt%283%29%29%2F13

Edwin