初2分式数学题(1/a+1/b)^2/(1/a^2-1/b^2)已知答案`求步骤`详细给分
问题描述：
初2分式数学题
(1/a+1/b)^2/(1/a^2-1/b^2)已知答案`求步骤`详细给分
答
分子通分得（A+B)*2/A*2B*2 分母通分（B*2-A*2)/A*2B*2 约分得（A+B)*2/(B*2-A*2) 约分（a+b）/(B-A)
答
(1/a+1/b)^2/(1/a^2-1/b^2)
=(1/a+1/b)(1/a+1/b)(1/a+1/b)(1/a-1/b)
=(1/a+1/b)^3(1/a-1/b)
因为(a+b)^3=a^3+b^3+3ba^2+3ab^2
=1/a^4-1/b^4+(2/a^3) *1/b-(2/a)*1/b^3
答
(1/a+1/b)^2/(1/a^2-1/b^2)
=(1/a+1/b)²/(1/a+1/b)(1/a-1/b)
=(1/a+1/b)/(1/a-1/b)
=(b+a)/(b-a)