Question

高一数学关于根式的题目~(x+y)/(根号下x+根号下y)+2xy/(x根号下y+y根号下x)=______.

(x+y)/(根号下x+根号下y)+2xy/(x根号下y+y根号下x)=______.
要过程~谢谢~

Answer 1

结果为根号下x+根号下y
解2xy/(x根号下y+y根号下x）分母提公因式根号下xy 然后前后两式分母都含根号下x+根号下y
合并后约分得根号下x+根号下y

Answer 2

(1)∵x√y+y√x=(√x+√y)×√(xy).∴2xy/(x√y+y√x)=(2√(xy)/(√x+√y).∴原式=（x+y)/(√x+√y)+(2√(xy)/(√x+√y)=(√x+√y)²/(√x+√y)=√x+√y.