Question

计算：（a/a-1+a/1-a）÷a/a-1；（x/x-2-x/x+2）÷4x/2-x.

Answer 1

（a/a-1+a/1-a）÷a/a-1
=（a/a-1-a/a-1）÷a/a-1
=0÷a/a-1
当a=1时
原式无意义
当a≠1时
原式=0

原式=(2-x)/4x-[(2-x)x]/[(x+2)x]
当x=0或-2或2时
原式无意义
当x≠0或±2时
原式=[(2-x)x]/[(x+2)x]-[(2-x)x]/[(x+2)x]
=0

Answer 2

（a/a-1+a/1-a）÷a/a-1；
=[a/(a-1)-a/(a-1)]×(a-1)/a
=0

（x/x-2-x/x+2）÷4x/2-x
=[x(x+2)/(x+2)(x-2)-x(x-2)/(x+2)(x-2)]×[-(x-2)/4x]
=(x²+2x-x²+2x)/(x+2)(x-2)×[-(x-2)/4x]
=4x/(x+2)(x-2)×[-(x-2)/4x]
=-1/(x+2)