How do you rationalize the denominator and simplify #(3sqrt2 + 2sqrt7)/( sqrt7 - 5sqrt2)#?

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Answer 1 · 2018-03-23T21:17:03

#-(44+13sqrt(14))/43#

We first multiply the numerator and the denominator of this fraction by the conjugate of the denominator.

The denominator is #sqrt(7)-5sqrt(2)#, so its conjugate is #sqrt(7)+5sqrt(2)#, Let's do the multiplication.

#(3sqrt(2)+2sqrt(7))/(sqrt(7)-5sqrt(2))*(sqrt(7)+5sqrt(2))/(sqrt(7)+5sqrt(2))#

#((3sqrt(2)+2sqrt(7))(sqrt(7)+5sqrt(2)))/((sqrt(7)-5sqrt(2))(sqrt(7)+5sqrt(2)))#

#(3sqrt(14)+15*2+2*7+10sqrt(14))/(7+5sqrt(14)-5sqrt(14)-25*2)#

Simplifying we have

#(44+13sqrt(14))/(-43)=-(44+13sqrt(14))/43#.