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

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

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

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

1/(sqrt3 + sqrt2) + 1/(sqrt3 -sqrt2)=

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

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

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

Show that (sqrt(7) + isqrt(3)) / (sqrt(7) - isqrt(3)) + (sqrt(7) - isqrt(3)) / (sqrt(7) + isqrt(3)) , is real.

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