Question

初中分式化简

（a²-2a分之a+2 + 4-a²分之8 ）÷a分之a-2
要求列出详细过程

Answer 1

（a²-2a分之a+2 + 4-a²分之8 ）÷a分之a-2
=[(a+2)/a(a-2)+8/(2+a)(2-a)]÷(a-2)/a
=[(a+2)/a(a-2)+8/(2+a)(2-a)]×a/(a-2)
=(a+2)/[a(a-2)]×a/(a-2)+8/[(2+a)(2-a)]×a/(a-2)
=a+2-8a/(a+2)
/表示分式中间的横

Answer 2

[(a+2)/(a^2-2a)+8/(4-a^2)]*a/a-2
=[(a+2)/a(a-2)-8/(a-2)(a+2)]*a/a-2
=[(a+2)(a+2)/a(a-2)(a+2)-8a/a(a-2)(a+2)]*a/a-2
=(a-2)(a-2)/a(a-2)(a+2)*a/a-2
=(a-2)/a(a+2)*a/a-2
=1/(a+2)

Answer 3

（a²-2a分之a+2 + 4-a²分之8 ）÷a分之a-2
=[(a+2)/a(a-2)-8/(a+2)(a-2)][(a-2)/a]
=[(a+2)/a²-8/a(a+2)]
=[(a+2)²-8a]/a²(a+2)
=(a-2)²/[a²(a+2)]