x=1/(√3-√2)=(√3+√2)/[(√3-√2)(√3+√2)]=(√3+√2)/[(√3)²-(√2)²]=(√3+√2)/[3-2]=√3+√2;
1/x=√3-√2,
√[(x-1/x)²+4]-√[(x+1/x)²-4]
=√[(√3+√2-√3+√2)²+4]-√[(√3+√2+√3-√2)²-4]
=√[(2√2)²+4]-√[(2√3)²-4]
=√[8+4]-√[12-4]
=2√3-2√2