求使(a²+ab)/(b-ab)除以(ab/2)*(b²-ab)/(a²-ab)具有正整数值的所有a的整数值

求使(a²+ab)/(b-ab)除以(ab/2)*(b²-ab)/(a²-ab)具有正整数值的所有a的整数值
求使(a²+ab)/(b-ab)除以(ab/2)*(b²-ab)/(a²-ab)具有正整数值的所有a的整数值

求使(a²+ab)/(b-ab)除以(ab/2)*(b²-ab)/(a²-ab)具有正整数值的所有a的整数值
(a²+ab)/(b-ab)÷(a+b)/2×(b²-ab)/(a²-ab)
=a(a+b)/b(1-a)×2/(a+b)×[-b(a-b)/a(a-b)]
=2a/(a-1)
=2(a-1+1)/(a-1)
=2[(a-1)/(a-1)+1/(a-1)]
=2[1+1/(a-1)]
=2+2/(a-1)是整数
则a-1是2的因数
所以a-1=1,-1,2,-2
a=2,a=0,a=3,a=-1
因为a²-ab=a(a-b)在分母
所以a≠0
所以a=2,a=3,a=-1

(a²+ab)/(b-ab)÷(a+b)/2×(b²-ab)/(a²-ab)
=a(a+b)/b(1-a)×2/(a+b)×[-b(a-b)/a(a-b)]
=2a/(a-1)
=2(a-1+1)/(a-1)
=2[(a-1)/(a-1)+1/(a-1)]
=2[1+1/(a-1)]
=2+2/(a-1)是整数
...

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(a²+ab)/(b-ab)÷(a+b)/2×(b²-ab)/(a²-ab)
=a(a+b)/b(1-a)×2/(a+b)×[-b(a-b)/a(a-b)]
=2a/(a-1)
=2(a-1+1)/(a-1)
=2[(a-1)/(a-1)+1/(a-1)]
=2[1+1/(a-1)]
=2+2/(a-1)是整数
则a-1是2的因数
所以a-1=1,-1,2,-2
a=2,a=0,a=3,a=-1
因为a²-ab=a(a-b)在分母
所以a≠0
所以a=2,a=3,a=-1

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a=2,a=3,a=-1