作业帮(1) b/(a-b) + a/(a+b)-2ab/(b^2-a^2)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/09/14 08:08:06
(1) b/(a-b) + a/(a+b)-2ab/(b^2-a^2)
(2) [1-1/(1-X) ] ÷X/X-1
(2) [1-1/(1-X) ] ÷X/X-1
(1) b/(a-b) + a/(a+b)-2ab/(b^2-a^2)
=(a+b)b/(a^2-b^2)+(a-b)a/(a^2-b^2)+2ab/(a^2-b^2)
=(ab+b^2+a^2-ab+2ab)/(a^2-b^2)
=(a^2+2ab+b^2)/(a^2-b^2)
=(a+b)^2/(a+b)(a-b)
=(a+b)/(a-b)
(2) [1-1/(1-X) ] ÷X/X-1
=(1-x-1)/(1-x)*(x-1)/x
=(-x)/(1-x)*(x-1)/x
=x/(x-1)*(x-1)/x
=1
=(a+b)b/(a^2-b^2)+(a-b)a/(a^2-b^2)+2ab/(a^2-b^2)
=(ab+b^2+a^2-ab+2ab)/(a^2-b^2)
=(a^2+2ab+b^2)/(a^2-b^2)
=(a+b)^2/(a+b)(a-b)
=(a+b)/(a-b)
(2) [1-1/(1-X) ] ÷X/X-1
=(1-x-1)/(1-x)*(x-1)/x
=(-x)/(1-x)*(x-1)/x
=x/(x-1)*(x-1)/x
=1
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