SOLUTION: The problem is: {{{ (x)/(4+ sqrt(2)) - (-1+ 3sqrt(2)) }}} i tried rationalizing the first part of the problem by multiplying it by the conjugate and then i distributed the ne

Algebra ->  Radicals -> SOLUTION: The problem is: {{{ (x)/(4+ sqrt(2)) - (-1+ 3sqrt(2)) }}} i tried rationalizing the first part of the problem by multiplying it by the conjugate and then i distributed the ne      Log On


   



Question 393898: The problem is:
+%28x%29%2F%284%2B+sqrt%282%29%29+-+%28-1%2B+3sqrt%282%29%29+
i tried rationalizing the first part of the problem by multiplying it by the conjugate and then i distributed the negative sign and then added but none of the terms were like...
please help me solve this!

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


+%28x%29%2F%284%2B+sqrt%282%29%29+-+%28-1%2B+3sqrt%282%29%29+

+%28x%2F%284%2B+sqrt%282%29%29%29+-+%28-1%2B+3sqrt%282%29%29+

Write the second term over 1

+%28x%2F%284%2B+sqrt%282%29%29%29+-+%28%28-1%2B+3sqrt%282%29%29%2F1%29+

Get an LCD of 4%2Bsqrt%282%29







+%28x%2F%284%2B+sqrt%282%29%29%29+-+%28%282%2B11sqrt%282%29%29%2F%284%2Bsqrt%282%29%29%29+

+%28x-%282%2B11sqrt%282%29%29%29%2F%284%2B+sqrt%282%29%29+

+%28x-2-11sqrt%282%29%29%2F%284%2B+sqrt%282%29%29+

Now rationalize the denominator:



Group the %28x-2%29 so you can use FOIL on top as well as the bottom:





%284x+-+8+-+x%2Asqrt%282%29+%2B+2sqrt%282%29+-+44sqrt%282%29+%2B+22%29%2F%2816-2%29

%284x-x%2Asqrt%282%29%2B14-42sqrt%282%29%29%2F14

You can leave it like the above or maybe

%284x%2B14-x%2Asqrt%282%29-42sqrt%282%29%29%2F14

and/or then maybe minimize the number of square roots 

%284x%2B14-sqrt%282%29%28x%2B42%29%29%2F14

Edwin