How do you rationalize the denominator and simplify #(5+sqrt3)/(2-sqrt3)#?

1 Answer
Alan P.
Dec 21, 2016

#color(green)(13+7sqrt(3))#

Explanation:

We can rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.

The conjugate of #(2-sqrt(3))# is #(2+sqrt(3))#

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

#color(white)("XXX")=(13+7sqrt(3))/(2^2-(sqrt(3))^2)=13+7sqrt(3)#

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