Simplify `((sqrt(7)+sqrt(3)))/((sqrt(7)-sqrt(3)))+((sqrt(7)-sqrt(3)))/((sqrt(7)+sqrt(3)))`

Show that (i)" "{((3+2i))/((2-3i))+((3-2i))/((2+3i))} is purely real, (ii)" "{((sqrt(7)+i sqrt(3)))/((sqrt(7)-i sqrt(3)))+((sqrt(7)- i sqrt(3)))/((sqrt(7) + i sqrt(3)))} is purely real.

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

(sqrt(5)+sqrt(3))(sqrt(7)-sqrt(3))

Simplify (sqrt(7)+sqrt(3))(3-sqrt(3))

Simplify (sqrt(7)+sqrt(2))(sqrt(7)-sqrt(2))

Simplify (sqrt(7))/(sqrt(2))+(3)/(sqrt(3))

Simplify (1)/(sqrt(7)+sqrt(3)-sqrt(2))

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

(sqrt(7)-sqrt(5))^3 - (sqrt(7)+sqrt(5))^3

given x=(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3)),y=(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3)) find the value of x^(4)+y^(4)+(x+y)^(4)