新包青天之梅花盗04:已知m/n=5/3,求m/m+n+m/m-n-n^2/m^2-n^2的值(写出过程,答案为41/16)
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m/(m+n)+m/(m-n)-n^2/(m^2-n^2)=(m/n)/(1+m/n)+(m/n)/(-1+m/n)-1/((m/n)^2-1)=(5/3)/(1+5/3)+(5/3)/(5/3-1)-1/(25/9-1)=5/8+5/2-9/16=41/16
m/n=5/3,如果是填空题就可以直接用m=5 n=3来代入求解,但是如果是解答题,最好还是规范一点,把m=5n/3代入原式得:
m/(m+n)+m/(m-n)-n^2/(m^2-n^2)=(5n/3)/[(5n/3)+n]+(5n/3)/[(5n/3)-n]-n^2/[(5n/3)^2-n^2]=41/16
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