若ab=1,则【a/(a+1)】+【b/(b+1)】的值为___.示例1:【a/(a+1)】+【b/(b+1)】=【a(b+1)+b(a+1)】/(a+1)(b+1)=(2ab+a+b)/(ab+a+b+1)=(2+a+b)/(2+a+b)=1 下面是小明的做法,但是被弄脏
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![若ab=1,则【a/(a+1)】+【b/(b+1)】的值为___.示例1:【a/(a+1)】+【b/(b+1)】=【a(b+1)+b(a+1)】/(a+1)(b+1)=(2ab+a+b)/(ab+a+b+1)=(2+a+b)/(2+a+b)=1 下面是小明的做法,但是被弄脏](/uploads/image/z/4027497-33-7.jpg?t=%E8%8B%A5ab%EF%BC%9D1%2C%E5%88%99%E3%80%90a%2F%EF%BC%88a%2B1%EF%BC%89%E3%80%91%2B%E3%80%90b%2F%EF%BC%88b%2B1%EF%BC%89%E3%80%91%E7%9A%84%E5%80%BC%E4%B8%BA___.%E7%A4%BA%E4%BE%8B1%EF%BC%9A%E3%80%90a%2F%EF%BC%88a%2B1%EF%BC%89%E3%80%91%2B%E3%80%90b%2F%EF%BC%88b%2B1%EF%BC%89%E3%80%91%3D%E3%80%90a%EF%BC%88b%2B1%EF%BC%89%2Bb%EF%BC%88a%2B1%EF%BC%89%E3%80%91%2F%EF%BC%88a%2B1%EF%BC%89%EF%BC%88b%2B1%EF%BC%89%3D%EF%BC%882ab%2Ba%2Bb%EF%BC%89%2F%EF%BC%88ab%2Ba%2Bb%2B1%EF%BC%89%3D%EF%BC%882%2Ba%2Bb%EF%BC%89%2F%EF%BC%882%2Ba%2Bb%EF%BC%89%3D1+%E4%B8%8B%E9%9D%A2%E6%98%AF%E5%B0%8F%E6%98%8E%E7%9A%84%E5%81%9A%E6%B3%95%2C%E4%BD%86%E6%98%AF%E8%A2%AB%E5%BC%84%E8%84%8F)
若ab=1,则【a/(a+1)】+【b/(b+1)】的值为___.示例1:【a/(a+1)】+【b/(b+1)】=【a(b+1)+b(a+1)】/(a+1)(b+1)=(2ab+a+b)/(ab+a+b+1)=(2+a+b)/(2+a+b)=1 下面是小明的做法,但是被弄脏
若ab=1,则【a/(a+1)】+【b/(b+1)】的值为___.
示例1:【a/(a+1)】+【b/(b+1)】
=【a(b+1)+b(a+1)】/(a+1)(b+1)
=(2ab+a+b)/(ab+a+b+1)
=(2+a+b)/(2+a+b)
=1
下面是小明的做法,但是被弄脏了一部分.如果方法错误,请指出.如果方法正确,请补全过程.(不可逆向将式子变回上述过程.)
【a/(a+1)】+【b/(b+1)】
=【a(b+1)+b(a+1)】/(a+1)(b+1)
=【1/(a+1)(b+1)】*【a(b+1)+b(a+1)】
={1/【(b+1)-(a+1)】}*【1/(a+1)-1/(b+1)】*【a(b+1)+b(a+1)】
=.
若ab=1,则【a/(a+1)】+【b/(b+1)】的值为___.示例1:【a/(a+1)】+【b/(b+1)】=【a(b+1)+b(a+1)】/(a+1)(b+1)=(2ab+a+b)/(ab+a+b+1)=(2+a+b)/(2+a+b)=1 下面是小明的做法,但是被弄脏
方法正确
【a/(a+1)】+【b/(b+1)】
=【a(b+1)+b(a+1)】/(a+1)(b+1)
=【1/(a+1)(b+1)】*【a(b+1)+b(a+1)】
={1/【(b+1)-(a+1)】}*【1/(a+1)-1/(b+1)】*【a(b+1)+b(a+1)】
={1/【(b+1)-(a+1)】}*{【(b+1)-(a+1)】/【(a+1)(b+1)】}*【a(b+1)+b(a+1)】
={1/【(b+1)-(a+1)】}*{【(b+1)-(a+1)】/(ab+a+b+1)}*(2ab+a+b)
={1/【(b+1)-(a+1)】}*【(b+1)-(a+1)】
=1