SOLUTION: Simplify: {{{((4+sqrt(5))(sqrt(5) -3)/(2-sqrt(5)))}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify: {{{((4+sqrt(5))(sqrt(5) -3)/(2-sqrt(5)))}}}      Log On


   

Question 866633: Simplify:
%28%284%2Bsqrt%285%29%29%28sqrt%285%29+-3%29%2F%282-sqrt%285%29%29%29
Answer by ben720(159) About Me  (Show Source):
You can put this solution on YOUR website!
%284%2Bsqrt%285%29%29%28sqrt%285%29+-3%29%2F%282-sqrt%285%29%29
First, use FOIL to multiply %284%2Bsqrt%285%29%29%28sqrt%285%29+-3%29
%284sqrt%285%29-3sqrt%285%29-12%2B5%29%2F%282-sqrt%285%29%29
%28sqrt%285%29-7%29%2F%282-sqrt%285%29%29
Multiply the expression by the conjugate of the denominator
%28sqrt%285%29-7%29%282%2Bsqrt%285%29%29%2F%282-sqrt%285%29%29%282%2Bsqrt%285%29%29
Multiply
%285-7sqrt%285%29%2B2sqrt%285%29-14%29%2F%284-sqrt%285%29%5E2%29
Simplify
%28-5sqrt%285%29-9%29%2F-1
Cancel out -1
sqrt%285%29%2B9