`([(sqrt(2)+isqrt(3))+(sqrt(2)-isqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])`

([(sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

(sqrt(3)-sqrt(2))(1)/(sqrt(3))

(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))

(1)/(sqrt(2)+sqrt(3))-(2)/(sqrt(5)-sqrt(3))+(3)/(sqrt(5)-sqrt(2))=

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

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

(1+sqrt(2))/(sqrt(5)+sqrt(3))+(1-sqrt(2))/(sqrt(5)-sqrt(3))

Perform the following by the indicated operations. Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : Prove that: [(sqrt(7)+isqrt(3))/(sqrt(7)-isqrt(3))+(sqrt(7)-isqrt(3))/(sqrt(7)+isqrt(3))] is real.

(2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)+1)/(sqrt(3)-1)is

sqrt(2)xx sqrt(3+sqrt(2)+sqrt(3))-1-sqrt(2)-sqrt(3)