Question

已知|2m-n除以m+2n|=3，求2（2m-n）除以m+2n-2m-n除以m+2n-3的值。

Answer 1

|2m-n除以m+2n|=3
2m-n除以m+2n=3或2m-n除以m+2n=-3
2m-n=3(m+2n)或2m-n+3(m+2n)=0
m=-7n 或m=n
(1)当m=-7n时
2（2m-n）除以m+2n-2m-n除以m+2n-3
=2（2*(-7n)-n）/(-7n+2n)-(2*(-7n)-n)/(-7n+2n-3)
=2（-15n）/(-5n)-(-15n)/(-5n-3)
=6-15n/5n+3
=30n+18-15n/5n+3
=15n+18/5n+3
=3+9/5n+3
(2)当m=n时
2（2m-n）除以m+2n-2m-n除以m+2n-3
=2（2*n-n）/(n+2n)-(2*n-n)/(n+2n-3)
=2（n）/(3n)-(n)/(3n-3)
=2/3-n/3n-3
=2n-2-n/3n-3
=n-2/3n-3