已知x为整数,且2/(x+3)+2/(3-x)+(2x-18)/(x^2-9)为整数,则所有符合条件的x的值的总和为是(2x-18)
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![已知x为整数,且2/(x+3)+2/(3-x)+(2x-18)/(x^2-9)为整数,则所有符合条件的x的值的总和为是(2x-18)](/uploads/image/z/3727688-32-8.jpg?t=%E5%B7%B2%E7%9F%A5x%E4%B8%BA%E6%95%B4%E6%95%B0%2C%E4%B8%942%2F%EF%BC%88x%2B3%29%2B2%2F%283-x%29%2B%282x-18%29%2F%28x%5E2-9%29%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%E7%9A%84%E5%80%BC%E7%9A%84%E6%80%BB%E5%92%8C%E4%B8%BA%E6%98%AF%282x-18%29)
已知x为整数,且2/(x+3)+2/(3-x)+(2x-18)/(x^2-9)为整数,则所有符合条件的x的值的总和为是(2x-18)
已知x为整数,且2/(x+3)+2/(3-x)+(2x-18)/(x^2-9)为整数,则所有符合条件的x的值的总和为
是(2x-18)
已知x为整数,且2/(x+3)+2/(3-x)+(2x-18)/(x^2-9)为整数,则所有符合条件的x的值的总和为是(2x-18)
2÷(x+3)+2÷(x-3)+(2x-18)÷(x2-9)
=2(1/(x+3) + 1/(x-3) + (x-9)/[(x+3)(x-3)])
=2 * 3 * (x-3)/[(x+3)(x-3)])
=6/(x+3)
设y=6/(x+3)
x=6/y - 3
因x为整数,所以6/y为整数,所以,y为6的因子:-6,-3,-2,-1,1,2,3,6
所以x解集为:-4,-5,-6,-9,0,-1,-2
则所有符合条件的x的值的总和为-27
原式=2(x-3-x-3)/(x+3)(x-3)+(2x+18)/(x+3)(x-3)
=(-12+2x+18)/(x+3)(x-3)
=2(x+3)/(x+3)(x-3)
=2/(x-3)是整数
所以x-3是2的约数
x-3=1,-1,2,-2
x=4,2,5,1
所以和=4+2+5+1=12
2÷(x+3)+2÷(x-3)+(2x-18)÷(x2-9)
=2(1/(x+3) + 1/(x-3) + (x-9)/[(x+3)(x-3)])
=2 * 3 * (x-3)/[(x+3)(x-3)])
=6/(x+3)
设y=6/(x+3)
x=6/y - 3
因x为整数,所以6/y为整数,所以,y为6的因子:-6,-3,-2,-1,1,2,3,...
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2÷(x+3)+2÷(x-3)+(2x-18)÷(x2-9)
=2(1/(x+3) + 1/(x-3) + (x-9)/[(x+3)(x-3)])
=2 * 3 * (x-3)/[(x+3)(x-3)])
=6/(x+3)
设y=6/(x+3)
x=6/y - 3
因x为整数,所以6/y为整数,所以,y为6的因子:-6,-3,-2,-1,1,2,3,6
所以符合要求的整数x为:-4,-5,-6,-9,0,-1,-2
则所有符合要求的x的值的总和为-27
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