Questions on Algebra: Radicals -- complicated equations involving roots answered by real tutors!

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Question 152697: Express in simplest form with rationalized denominators: sqrt 7 - sqrt 5 / sqrt 5 + 3 sqrt 7: Express in simplest form with rationalized denominators: sqrt 7 - sqrt 5 / sqrt 5 + 3 sqrt 7
Answer by jim_thompson5910(9162) About Me  (Show Source):
You can put this solution on YOUR website!
(sqrt(7) - sqrt(5)) / (sqrt(5) + 3*sqrt(7)) Start with the given expression.



((sqrt(7) - sqrt(5)) / (sqrt(5) + 3*sqrt(7)))((sqrt(5) - 3*sqrt(7))/(sqrt(5) - 3*sqrt(7))) Multiply both numerator and denominator by sqrt(5) - 3*sqrt(7)


((sqrt(7) - sqrt(5))(sqrt(5) - 3*sqrt(7))) / ((sqrt(5) + 3*sqrt(7))(sqrt(5) - 3*sqrt(7))) Combine the fractions



(sqrt(7)sqrt(5)- 3*sqrt(7)sqrt(7) - sqrt(5)sqrt(5)+3*sqrt(5)sqrt(7)) / (sqrt(5)sqrt(5)-3*sqrt(5)sqrt(7)+3*sqrt(5)sqrt(7)-3*3*sqrt(7)sqrt(7)) FOIL



(sqrt(35)- 3*7 - 5+3*sqrt(35)) / (5-3*sqrt(35)+3*sqrt(35)-9*7) Combine and multiply the roots.



(-26+4*sqrt(35)) / (-58) Combine like terms


(13-2*sqrt(35)) / (29) Reduce


So (sqrt(7) - sqrt(5)) / (sqrt(5) + 3*sqrt(7))=(13-2*sqrt(35)) / (29)