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如果f(t)=t/(1+t),g(t)=t/(1-t),证明：f(t)-g(t)=-2g（t²）
题目详情
如果f(t)=t/(1+t),g(t)=t/(1-t) ,证明：f(t)-g(t)=-2g（t²）
▼优质解答
答案和解析
f(t)-g(t)
=t/(1+t)-t/(1-t)
=t/(1+t)+t/(t-1)
=[t(t-1)/(1+t)(t-1)]+[t(t+1)/(t+1)(t-1)]
=(t²-t+t²+t)/(t+1)(t-1)
=2t²/(t²-1)
-2g(t²)
=-2t²/(1-t²)
=2t²/(t²-1)
左边等于右边
所以f(t)-g(t)=-2g（t²）成立
得证
=t/(1+t)-t/(1-t)
=t/(1+t)+t/(t-1)
=[t(t-1)/(1+t)(t-1)]+[t(t+1)/(t+1)(t-1)]
=(t²-t+t²+t)/(t+1)(t-1)
=2t²/(t²-1)
-2g(t²)
=-2t²/(1-t²)
=2t²/(t²-1)
左边等于右边
所以f(t)-g(t)=-2g（t²）成立
得证
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