已知:m/n=5/3,求(m/m+n)+(m/m-n)-(n²/m²-n²)的值
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已知:m/n=5/3,求(m/m+n)+(m/m-n)-(n²/m²-n²)的值
已知:m/n=5/3,求(m/m+n)+(m/m-n)-(n²/m²-n²)的值
已知:m/n=5/3,求(m/m+n)+(m/m-n)-(n²/m²-n²)的值
m/(m+n)+m/(m-n)-n²/(m²-n²)
=[m(m-n)+m(m+n)]/(m²-n²) -n²/(m²-n²)
=(2m²-n²)/(m²-n²)
=(m²+m²-n²)/(m²-n²)
=1+m²/(m²-n²)
=1+1/[1-(n/m)²]
=1+1/[1-(3/5)²]
=41/16
因为m/n=5/3,∴设m5k,n3k.(m/m+n)+(m/m-n)-(n²/m²-n²)=(1+3k)+(1-3K)-(9k的平方分之25k的平方-9k的平方)=-25k的平方
m/n=5/3 => n!=0且m!=0,所以 m=(5n)/3 或是n=(3m)/5 带入所求式子
得 m/(m+n) + m/(m-n) - n^2/(m^2-n^2) = m/(m+3m/5) + m/(m-3m/5) - n^2/[(5n/3)^2-n^2]
化简得 原式=5/8 + 5/2 - 9/16 = 41/16
计算结果可能不正确建议您自己算一下....
m/(m+n)+m/(m-n)-n²/(m²-n²)
=[m(m-n)+m(m+n)]/(m²-n²) -n²/(m²-n²)
=(2m²-n²)/(m²-n²)
=[2(m/n)²-1]/[(m/n)²-1]
=(m/n)²/[(m/n)²-1]-1
=(25/9)/(25/9-1) - 1
=9/16