作业帮一个数学很简单化简题.
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/15 15:27:26
一个数学很简单化简题.
（k+1）x=(k-1)y+2K怎么到y+1=(k+1)(x-1)/(k-1),(k不等于1)
（k+1）x=(k-1)y+2K怎么到y+1=(k+1)(x-1)/(k-1),(k不等于1)
【详细过程】
(k+1)x=(k-1)y+2k
将等式移项
(k+1)x-2k=(k-1)y
由于k≠1,将上式两边同时除以k-1
y=[(k+1)x-2k]/(k-1)
y=[(k+1)x/(k-1)]-[2k/(k-1)]
两边同时加1得
y+1=[(k+1)x/(k-1)]-[2k/(k-1)]+1
y+1=[(k+1)x/(k-1)]-[2k/(k-1)]+[(k-1)/(k-1)]
y+1=[(k+1)x/(k-1)]-[(-1-k)/(k-1)]
y+1=[(k+1)x/(k-1)]+[(1+k)/(k-1)]
对右边提取公因式k+1得
y+1=(1+k)(x+1)/(k-1)
(k+1)x=(k-1)y+2k
将等式移项
(k+1)x-2k=(k-1)y
由于k≠1,将上式两边同时除以k-1
y=[(k+1)x-2k]/(k-1)
y=[(k+1)x/(k-1)]-[2k/(k-1)]
两边同时加1得
y+1=[(k+1)x/(k-1)]-[2k/(k-1)]+1
y+1=[(k+1)x/(k-1)]-[2k/(k-1)]+[(k-1)/(k-1)]
y+1=[(k+1)x/(k-1)]-[(-1-k)/(k-1)]
y+1=[(k+1)x/(k-1)]+[(1+k)/(k-1)]
对右边提取公因式k+1得
y+1=(1+k)(x+1)/(k-1)