SOLUTION: Simplify and rationalize the expression giving your answer in the forma+b√c, where a, b and c are constants 11/(7-√3)-5/(7+√3)

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Question 1199170: Simplify and rationalize the expression giving your answer in the forma+b√c, where a, b and c are constants
11/(7-√3)-5/(7+√3)
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify and rationalize the expression giving your answer in the forma+b√c, where a, b and c are constants
11/(7-√3)-5/(7+√3)
Assume it is:
11%2F%28%287-sqrt%283%29%29%29 - 5%2F%28%287%2Bsqrt%283%29%29%29
find the common denominator; FOIL (7-sqrt(3))*(7+sqrt(3))
middle terms cancel so we have 49-3 = 46 is the common denominator
so we have
%2811%287%2Bsqrt%283%29%29+-+5%287-sqrt%283%29%29%29%2F46 = %2877%2B+11sqrt%283%29+-+35+%2B+5sqrt%283%29%29%2F46
combine like terms, reduce the fraction
%2842+%2B+16sqrt%283%29%29%2F46 = %2821+%2B+8sqrt%283%29%29%2F23

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of doing it for you, 

here's one that's exactly like yours step-by-step:

13%2F%2811-sqrt%285%29%29-7%2F%2811%2Bsqrt%285%29%29



%28143%2B13sqrt%285%29-77%2B7sqrt%285%29%29%2F%28121-5%29

%2866%2B20sqrt%285%29%29%2F116

%282%2833%2B10sqrt%285%29%29%29%2F116

%2833%2B10sqrt%285%29%29%2F58

33%2F58%2Bexpr%2810%2F58%29sqrt%285%29

33%2F58%2Bexpr%285%2F29%29sqrt%285%29

That is in the form a%2Bb%2Asqrt%28c%29 where a=33%2F58, b=5%2F29, c=5

Edwin