【{初三数学}】化简求值!{(x+2根号xy+y)/根号x+根号y}+{1/(根号x-根号y)}除以{(x-y+1)/根号x}比较难看,列出来就能看了,求值就不用了,只需要化简的过程.过程一定要清楚.谢谢了!

问题描述:

【{初三数学}】化简求值!
{(x+2根号xy+y)/根号x+根号y}+{1/(根号x-根号y)}除以{(x-y+1)/根号x}
比较难看,列出来就能看了,求值就不用了,只需要化简的过程.
过程一定要清楚.谢谢了!

{[(x+2√xy+y)/(√x+√y)]+[1/(√x-√y)]}/{(x-y+1)/√x}
={[(√x+√y)^2/(√x+√y)]+[(√x+√y)/(x-y)]}/{(x-y+1)√x/x}
={(√x+√y)+[(√x+√y)/(x-y)]}/{(x-y+1)√x/x}
={(√x+√y)[1+1/(x-y)]}/{(x-y+1)√x/x}
={(√x+√y)[(x-y+1)/(x-y)]}/{(x-y+1)√x/x}
=(√x+√y)[1/(x-y)]/[√x/x]
=√x(√x+√y)/(x-y)
=(x+√xy)/(x-y)