已知X为整数,并且X能使分式2/(X+2)+2/(3-X)+(2X+18)/(X²-9)的值也是整数,求出所有符合要求的整数救救我啊上面的打错了题目是已知X为整数,并且X能使分式2/(X+3)+2/(3-X)+(2X+18)/(X²-9)的值
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![已知X为整数,并且X能使分式2/(X+2)+2/(3-X)+(2X+18)/(X²-9)的值也是整数,求出所有符合要求的整数救救我啊上面的打错了题目是已知X为整数,并且X能使分式2/(X+3)+2/(3-X)+(2X+18)/(X²-9)的值](/uploads/image/z/2534876-44-6.jpg?t=%E5%B7%B2%E7%9F%A5X%E4%B8%BA%E6%95%B4%E6%95%B0%2C%E5%B9%B6%E4%B8%94X%E8%83%BD%E4%BD%BF%E5%88%86%E5%BC%8F2%2F%EF%BC%88X%2B2%EF%BC%89%2B2%2F%283-X%29%2B%282X%2B18%29%2F%28X%26sup2%3B-9%29%E7%9A%84%E5%80%BC%E4%B9%9F%E6%98%AF%E6%95%B4%E6%95%B0%2C%E6%B1%82%E5%87%BA%E6%89%80%E6%9C%89%E7%AC%A6%E5%90%88%E8%A6%81%E6%B1%82%E7%9A%84%E6%95%B4%E6%95%B0%E6%95%91%E6%95%91%E6%88%91%E5%95%8A%E4%B8%8A%E9%9D%A2%E7%9A%84%E6%89%93%E9%94%99%E4%BA%86%E9%A2%98%E7%9B%AE%E6%98%AF%E5%B7%B2%E7%9F%A5X%E4%B8%BA%E6%95%B4%E6%95%B0%EF%BC%8C%E5%B9%B6%E4%B8%94X%E8%83%BD%E4%BD%BF%E5%88%86%E5%BC%8F2%2F%EF%BC%88X%2B3%EF%BC%89%2B2%2F%283-X%29%2B%282X%2B18%29%2F%28X%26sup2%3B-9%29%E7%9A%84%E5%80%BC)
已知X为整数,并且X能使分式2/(X+2)+2/(3-X)+(2X+18)/(X²-9)的值也是整数,求出所有符合要求的整数救救我啊上面的打错了题目是已知X为整数,并且X能使分式2/(X+3)+2/(3-X)+(2X+18)/(X²-9)的值
已知X为整数,并且X能使分式2/(X+2)+2/(3-X)+(2X+18)/(X²-9)的值也是整数,求出所有符合要求的整数
救救我啊
上面的打错了
题目是已知X为整数,并且X能使分式2/(X+3)+2/(3-X)+(2X+18)/(X²-9)的值也是整数,求出所有符合要求的整数
已知X为整数,并且X能使分式2/(X+2)+2/(3-X)+(2X+18)/(X²-9)的值也是整数,求出所有符合要求的整数救救我啊上面的打错了题目是已知X为整数,并且X能使分式2/(X+3)+2/(3-X)+(2X+18)/(X²-9)的值
2/(X+3)+2/(3-X)+(2X+18)/(X²-9)
(2(3-x)+2(3+x))/(9- X²)+(2X+18)/(X²-9)
=(12-2X-18)/(9- X²)
= -2(x+3)/((3+x)(3-x)
= -2/(3-x)
要2/(3-x)是整数,因此3-x必须是2的约数,即3-x=正负1或者正负2
也就是x可以取值的数是1,2,4,5
2/(X+3)+2/(3-X)+(2X+18)/(X²-9)
=12/(9-X^2)+(2X+18)/(X²-9)
=(2X+6)/(x^2-9)
=2/(x-3)
那么x=1,2,4,5