作业帮已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?
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![已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?](/uploads/image/z/3834312-24-2.jpg?t=%E5%B7%B2%E7%9F%A5x%E4%B8%BA%E6%95%B4%E6%95%B0%2C%E4%B8%94%5B2%2F%28x%2B3%29%5D%2B%5B2%2F%283-x%29%5D%2B%5B%282x%2B18%29%2F%28x2-9%29%5D%E4%B8%BA%E6%95%B4%E6%95%B0%2C%E5%88%99%E6%89%80%E6%9C%89%E7%AC%A6%E5%90%88%E6%9D%A1%E4%BB%B6%E7%9A%84x%E5%80%BC%E7%9A%84%E5%92%8C%E4%B8%BA%E5%A4%9A%E5%B0%91%3F)
已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?
已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?
已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?
2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)
=2(x+3+3-x)/(x+3)(3-x)+(2x+18)/(x+3)(x-3)
=[12-(2x+18)]/(x+3)(3-x)
=2(x+3)/(x+3)(x-3)
=2/(x-3)
=>(x-3)=+-1,+-2
x=4,2,5,1,
1+2+4+5=12