化简:(根号x+根号y分之根号x)+(根号x-根号y分之根号y),并求当x=(根号3)y时的值。 谢谢,帮帮我!
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x=√3y
√x/(√x+√y)+√y/(√x-√y)
=√x(√x-√y)/[(√x+√y)(√x-√y)]+√y(√x+√y)/[(√x+√y)(√x-√y)]
=(x-√xy)/(x-y)+(√xy+y)/(x-y)
=(x-√xy+√xy+y)/(x-y)
=(x+y)/(x-y)
=(√3y+y)/(√3y-y)
=(√3+1)/(√3-1)
=(√3+1)^2/[(√3-1)(√3+1)]
=(4+2√3)/2
=2+√3
√x/(√x+√y)+√y/(√x-√y)
=√x(√x-√y)/[(√x+√y)(√x-√y)]+√y(√x+√y)/[(√x+√y)(√x-√y)]
=(x-√xy)/(x-y)+(√xy+y)/(x-y)
=(x-√xy+√xy+y)/(x-y)
=(x+y)/(x-y)
=(√3y+y)/(√3y-y)
=(√3+1)/(√3-1)
=(√3+1)^2/[(√3-1)(√3+1)]
=(4+2√3)/2
=2+√3
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