Question

【｛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

Answer 1

{[(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）