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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