SOLUTION: Simplify the expression. Rationalize the denominator. Assume that any variables are positive. What is {{{5/(3-2sqrt(6))}}} Thanks for the help. Steven

Algebra ->  Radicals -> SOLUTION: Simplify the expression. Rationalize the denominator. Assume that any variables are positive. What is {{{5/(3-2sqrt(6))}}} Thanks for the help. Steven       Log On


   

Question 115680This question is from textbook Algebra 2
: Simplify the expression. Rationalize the denominator. Assume that any variables are positive. What is 5%2F%283-2sqrt%286%29%29 Thanks for the help. Steven This question is from textbook Algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%283-2sqrt%286%29%29 Start with the given expression


%285%2F%283-2sqrt%286%29%29%29%28%283%2B2sqrt%286%29%29%2F%283%2B2sqrt%286%29%29%29 Multiply the fraction by %283%2B2sqrt%286%29%29%2F%283%2B2sqrt%286%29%29. Note: 3%2B2sqrt%286%29 is the conjugate of the denominator



5%283%2B2sqrt%286%29%29%2F%28%283-2sqrt%286%29%29%283%2B2sqrt%286%29%29%29 Combine the fractions


%2815%2B10sqrt%286%29%29%2F%28%283-2sqrt%286%29%29%283%2B2sqrt%286%29%29%29 Distribute


%2815%2B10sqrt%286%29%29%2F%289%2B6sqrt%286%29-6sqrt%286%29-4sqrt%286%29sqrt%286%29%29%29 Foil



%2815%2B10sqrt%286%29%29%2F%289%2B6sqrt%286%29-6sqrt%286%29-4%286%29%29%29 Multiply


%2815%2B10sqrt%286%29%29%2F%289-4%286%29%29%29 Combine like terms


%2815%2B10sqrt%286%29%29%2F%289-24%29%29 Multiply


%2815%2B10sqrt%286%29%29%2F%28-15%29%29 Subtract


%2815%29%2F%28-15%29%2B%2810sqrt%286%29%29%2F%28-15%29%29 Break up the fraction


-1-2sqrt%286%29%2F3%29 Reduce