[√(x1+1)-√(x2+1)] – [√(x1-1) – √(x2-1)]
={[√(x1+1)-√(x2+1)]*[√(x1+1)+√(x2+1)]/[√(x1+1)+√(x2+1)]}
-{[√(x1-1)-√(x2-1)]*[√(x1-1)+√(x2-1)]/[√(x1-1)+√(x2-1)]}
(注:这里用到平方差公式,也叫分子有理化)
=[(x1+1)-(x2+1)]/[√(x1+1)+√(x2+1)]
-[(x1-1)-(x2-1)]/[√(x1-1)+√(x2-1)]
= (x1-x2)/[√(x1+1) + √(x2+1)] - (x1-x2)/[√(x2-1)+√(x1-1)]