Question

化简[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1

要详细过程！
（2）、已知X为整数，且2/(x+3)+2/(3-x)+(2x+18)/(x＾2-9)为整数，求所有符合条件的X的值

Answer 1

1)原式=[ab/(a-b)^2]/[ab/(a+b)(a-b)]+1
=(a+b)(a-b)/(a-b)^2+1
=(a+b)/(a-b)+1
=2a/(a-b)
2)化简原式=[2(x-3)-2(x+3)+2x+18]/(x^2-9)
=2(x+3)/(x+3)(x-3)
=2/(x-3)
为整数
则x-3=-2或-1或1或2
x=1,2,4或5

Answer 2

[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1
=[a/(a-b)-a²/(a-b)²]÷[a/(a+b)-a²/(a+b)(a-b)]+1
=[a(a-b)/(a-b)²-a²/(a-b)²]÷[a(a-b)/(a+b)(a-b)-a²/(a+b)(a-b)]+1
=[(a²-ab)/(a-b)²-a²/(a-b)²]÷[(a²-ab)/(a+b)(a-b)-a²/(a+b)(a-b)]+1
=-ab/(a-b)²÷[(-ab)/(a+b)(a-b)]+1
=-ab/(a-b)²×(a+b)(a-b)/(-ab)+1
=(a+b)/(a-b)+1
=(a+b)/(a-b)+(a-b)/(a-b)
=2a/(a-b)

Answer 3

[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1
=[a/(a-b)-(a＾2)/(a-b)^2]÷[a/(a+b)-(a＾2)/(a-b)(a+b)]+1
=[a(a-b)/(a-b)^2-(a＾2)/(a-b)^2]÷[a(a-b)/(a+b)(a-b)-(a＾2)/(a-b)(a+b)]+1
=[(a^2-ab-a^2)/(a-b)^2]÷[(a^2-ab-a^2)/a-b)(a+b)]+1
=[-ab/(a-b)^2÷[(-ab)(a+b)(a-b)]+1
=-ab/(a-b)^2×(a+b)(a-b)/(-ab)+1
=(a+b)/(a-b)+1

Answer 4

[a/(a-b)-(a²)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1
=[a(a-b)/(a-b)²-a²/(a-b)²]÷[a(a-b)/(a+b)(a-b)-a²/(a+b)(a-b)]+1
={[a(a-b)-a²]/(a-b)²}×{(a+b)(a-b)/[a(a-b)-a²]}+1
=(a+b)/(a-b)+1
=2a/(a-b)

Answer 5

[a/(a-b)-(a²)/(a²-2ab+b²)]÷[a/(a+b)-(a²)/(a²-b²)]+1=[a(a-b)/(a-b)²-(a²)/(a²-2ab+b²)]÷[a(a-b)/(a²-b²)-(a²)/(a²-b²)]+1=[-ab/(a-b)²]÷[-ab/(a²-b²)]+1=(a+b)/(a-b)+1=2a/(a-b)