作业帮化简[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1（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
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 05:00:40
![化简[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1（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](/uploads/image/z/8794970-26-0.jpg?t=%E5%8C%96%E7%AE%80%5Ba%2F%28a-b%29-%28a%EF%BC%BE2%29%2F%28a%EF%BC%BE2-2ab%2Bb%EF%BC%BE2%29%5D%C3%B7%5Ba%2F%28a%2Bb%29-%28a%EF%BC%BE2%29%2F%28a%EF%BC%BE2-b%EF%BC%BE2%29%5D%2B1%EF%BC%882%EF%BC%89%E3%80%81%E5%B7%B2%E7%9F%A5X%E4%B8%BA%E6%95%B4%E6%95%B0%EF%BC%8C%E4%B8%942%2F%28x%2B3%29%2B2%2F%283-x%29%2B%282x%2B18%29%2F%28x%EF%BC%BE2-9%29%E4%B8%BA%E6%95%B4%E6%95%B0%EF%BC%8C%E6%B1%82%E6%89%80%E6%9C%89%E7%AC%A6%E5%90%88%E6%9D%A1%E4%BB%B6%E7%9A%84X%E7%9A%84%E5%80%BC)
化简[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1（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
化简[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1
（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
化简[a/(a-b)-(a＾2)/(a＾2-2ab+b＾2)]÷[a/(a+b)-(a＾2)/(a＾2-b＾2)]+1（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
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
[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+...
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[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)
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[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)
[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)
[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^...
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[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
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