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已知x为整数,且2 x+3 +2 3?x +2x+18 x2?9 为整数,求所有符合条件的x的值.

发布时间:2019-09-17

(x²-9)]
=2/(x+3)]+[2/[2/(3-x)]+[(2x+18)/(x-3)
∵x为整数且2/

回复:

回复:

2/x+3+2/3-x+2x+18/x^2-9
=[2(X-3)-2(X+3)+2X+18]/(X+3)(X-3)
=2(X+3)/(X+3)(X-3)
=2/(X-3)
∴X-3=±1, ±2
∴X=4,, 2, 5, 1
符合条件x的值的和为4+2+5+1=12

回复:

2/(x+3)+2/(3-x)+(2x+18)/(x^2-9)
=2/(x+3)-2/(x-3)+(2x+18)/(x^2-9)
=2(x-3)/(x^2-9)-2(x+3)/(x^2-9)+(2x+18)/(x^2-9)
=(2x-6-2x-6+2x+18)/(x^2-9)
=(2x+6)/(x^2-9)
=2(x+3)/(x-3)(x+3)
=2/(x-3).

回复:

[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x²-9)] =2/(x-3) ∵x为整数且2/(x-3)也是整数 ∴∴x-3=±2或±1 则x=5或1或4或2 5+1+4+2=12

回复:

2/(x+3)+2/(3-x)+(2x+18)/(x^2-9) =2/(x+3)-2/(x-3)+(2x+18)/(x^2-9) =2(x-3)/(x^2-9)-2(x+3)/(x^2-9)+(2x+18)/(x^2-9) =(2x-6-2x-6+2x+18)/(x^2-9) =(2x+6)/(x^2-9) =2(x+3)/(x-3)(x+3) =2/(x-3).

回复:

2/x+3+2/3-x+2x+18/x^2-9 =[2(X-3)-2(X+3)+2X+18]/(X+3)(X-3) =2(X+3)/(X+3)(X-3) =2/(X-3) ∴X-3=±1, ±2 ∴X=4,, 2, 5, 1 符合条件x的值的和为4+2+5+1=12

回复:

2/(x+3)+2/(3-x)+(2x+18)/(x^2-9) =[2(x-3)-2(x+3)+(2x+18)]/(x^2-9) =(2x+6)/(x^2-9) =2/(x-3)为整数 所以,x-3=2,1,-1,-2 x=5,4,2,1

回复:

2/(x+3)+2/(3-x)+(2x+18)/(x^2-9) =2/(x+3)-2/(x-3)+(2x+18)/(x^2-9) =2(x-3)/(x^2-9)-2(x+3)/(x^2-9)+(2x+18)/(x^2-9) =(2x-6-2x-6+2x+18)/(x^2-9) =(2x+6)/(x^2-9) =2(x+3)/(x-3)(x+3) =2/(x-3). 因此,x - 3 必然是2的因数, 2有4个因数, 1, ...

回复:

原式=2/(x+3)-2/(x-3)+(2x-18)/(x+3)(x-3) =(2x-6-2x-6+2x+18)/(x+3)(x-3) =(2x+6)/(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

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