Question

计算过程(根号(ab)-ab/(a+根号ab))÷(根号(ab)-b)/(a-b)(a>0,b>0)

Answer 1

[√(ab)-ab]/[a+√(ab)]÷[√(ab)-b]/(a-b)

=[√(ab)-ab]/[a+√(ab)]×(a-b)/[√(ab)-b]

=[√(ab)-ab](a-b)/{[a+√(ab)][√(ab)-b]}

=[√(ab)-ab](a-b)/{√a(√a+√b)×√b(√a-√b)}

=[√(ab)-ab](a-b)/{√(ab)(√a+√b)(√a-√b)}

=[√(ab)-ab](a-b)/{√(ab)(a-b)}

=[√(ab)-ab]/√(ab)

=√(ab)[1-√(ab)]/√(ab)

=1-√(ab)