Multiplication by the conjugate quantity :
mult_conjugate

mult_conjugate takes as argument an expression with a denominator or a numerator supposed to contain a square root :

• if the denominator contains a square root,
  mult_conjugate multiplies the numerator and the denominator of the expression by the conjugate quantity of the denominator.
• otherwise, if the numerator contains a square root,
  mult_conjugate multiplies the numerator and the denominator of this expression by the conjugate quantity of the numerator.

Input :

mult_conjugate((2+sqrt(2))/(2+sqrt(3)))

Output :

(2+sqrt(2))*(2-sqrt(3))/((2+sqrt(3))*(2-sqrt(3)))

Input :

mult_conjugate((2+sqrt(2))/(sqrt(2)+sqrt(3)))

Output :

(2+sqrt(2))*(-sqrt(2)+sqrt(3))/

((sqrt(2)+sqrt(3))*(-sqrt(2)+sqrt(3)))

Input :

mult_conjugate((2+sqrt(2))/2)

Output :

(2+sqrt(2))*(2-sqrt(2))/(2*(2-sqrt(2)))