(a+2根号ab+b)/(a-b) 减去 {[根号a/(a+根号ab)减去 根号b/(b-根号ab)]}除以根号a/(b
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/04/29 20:55:18
(a+2根号ab+b)/(a-b) 减去 {[根号a/(a+根号ab)减去 根号b/(b-根号ab)]}除以根号a/(b+根号ab)
(a+2根号ab+b)/(a-b) 减去 {[根号a/(a+根号ab)减去 根号b/(b-根号ab)]}除以根号a/(b+根号ab)
=(√a+√b)^2/(a-b)- {[√a/(a+√ab)- √b/(b-√ab)]}/√a/(b+√ab)
=(√a+√b)^2/(a-b)- {[√a(b-√ab)-(a+√ab) √b/(a+√ab)(b-√ab)]}/√a/(b+√ab)
=(√a+√b)^2/(a-b)- {[b√a-a√b-a√b-b√a) /(a+√ab)(b-√ab)]}/√a/(b+√ab)
=(√a+√b)^2/(a-b)- {[-2a√b /√a(√a+√b)√b(√b-√a)]}*√b(√b+√a)/√a
=(√a+√b)^2/(a-b)- {[2√a/(a-b)]}*√b(√b+√a)/√a
=(√a+√b)^2/(a-b)- 2√b(√b+√a)/(a-b)
=(a+2√ab+b- 2b-2√ab)/(a-b)
=(a-b)/(a-b)
=1
=(√a+√b)^2/(a-b)- {[√a/(a+√ab)- √b/(b-√ab)]}/√a/(b+√ab)
=(√a+√b)^2/(a-b)- {[√a(b-√ab)-(a+√ab) √b/(a+√ab)(b-√ab)]}/√a/(b+√ab)
=(√a+√b)^2/(a-b)- {[b√a-a√b-a√b-b√a) /(a+√ab)(b-√ab)]}/√a/(b+√ab)
=(√a+√b)^2/(a-b)- {[-2a√b /√a(√a+√b)√b(√b-√a)]}*√b(√b+√a)/√a
=(√a+√b)^2/(a-b)- {[2√a/(a-b)]}*√b(√b+√a)/√a
=(√a+√b)^2/(a-b)- 2√b(√b+√a)/(a-b)
=(a+2√ab+b- 2b-2√ab)/(a-b)
=(a-b)/(a-b)
=1
(a+2根号ab+b)/(a-b) 减去 {[根号a/(a+根号ab)减去 根号b/(b-根号ab)]}除以根号a/(b
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