SOLUTION: Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. Have to show work. Square root of a + square root of b (over)/ square root o

Algebra ->  Radicals -> SOLUTION: Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. Have to show work. Square root of a + square root of b (over)/ square root o      Log On


   

Question 1005571: Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. Have to show work.
Square root of a + square root of b (over)/ square root of a - square root of b
So equation looks like this
/a + /b
__________
/a - /b
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
%28sqrt%28a%29+%2B+sqrt%28b%29%29%2F%28sqrt%28a%29+-+sqrt%28b%29%29 =     <-----   multiply the numerator and denominator by   sqrt%28a%29+%2B+sqrt%28b%29.  You will get

=     <-----   apply the formula   (x+y)*(x-y) = x%5E2+-+y%5E2   to the denominator. Also open the parenteses in the numerator You will get

= %28a+%2B+2%2Asqrt%28a%29%2Asqrt%28b%29+%2B+b%29%2F%28a+-+b%29 = %28a+%2B+2%2Asqrt%28a%2Ab%29+%2B+b%29%2F%28a+-+b%29.

That's all.