Rationalise the denominator of 1/(4 + sqrt(3))

This denominator is irrational because it contains a surd. To rationalise the denominator we multiply the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of the denominator is 4-sqrt(3)Therefore we get 1/(4 + sqrt(3)) * (4 - sqrt(3))/(4 - sqrt(3)). This simplifies to: (4 - sqrt(3))/(16 + 4sqrt(3) - 4sqrt(3) -3) and therefore: (4 - sqrt(3))/13