Question

已知当x=8,y=18,求(x+y)/(根号x-根号y)-（2xy）/（x根号y-y根号x）

Answer 1

原式=(x+y)/(√x-√y)-(2xy)/(x√y-y√x)

=(x+y)/(√x-√y)-(2xy)/[√(xy)(√x-√y)]

=(x+y)/(√x-√y)-2√(xy)/(√x-√y)]

=[(x+y)-2√(xy)]/(√x-√y)

=[x-2√(xy)+y]/(√x-√y)

=(√x-√y)²/(√x-√y)

=√x-√y

当x=8,y=18时

原式=√8-√18

=2√2-3√2

= -√2