Question

大家帮帮忙哈，，急求！！！！谢谢了！！！化简：m/m -n 减 n/m+n 加 2mn/m平方减n平方

Answer 1

m/(m -n)- n/(m+n)+2mn/(m^2-n^2)
=[m(m+n)-n(m-n)+2mn]/(m+n)(m-n)
=[m^2+2mn+n^2]/(m+n)(m-n)
=(m+n)^2/(m+n)(m-n)
=(m+n)/(m-n)

Answer 2

直接算，同分，m^2-n^2=(m+n)(m-n)，得
m(m+n)/(m^2-n^2)-n(m-n)/(m^2-n^2)+2mn/(m^2-n^2)=(m^2+n^2)/(m^2-n^2)

Answer 3

由题意可得；m/(m -n)- n/(m+n)+2mn/(m^2-n^2)
=[m(m+n)-n(m-n)+2mn]/(m+n)(m-n)
=[m^2+2mn+n^2]/(m+n)(m-n)
=(m+n)^2/(m+n)(m-n)
=(m+n)/(m-n)

Answer 4

m/(m-n)-n/(m+n)+2mn/(m²-n²)=[m(m+n)]/[(m-n)(m+n)]-[n(m-n)]/[(m-n)(m+n)]+2mn/[(m-n)(m+n)]=[m(m+n)-n(m-n)+2mn]/[(m-n)(m+n)]=(m²+mn-mn+n²+2mn)/[(m-n)(m+n)]=(m+n)²/[(m-n)(m+n)]=(m+n)/(m-n)