1/a+1/b=1/(a+b) 求b/a+a/b的值
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1/a+1/b=1/(a+b) 求b/a+a/b的值
化简求值 (2a)/(a²-4) +1/( 2-a) a=1/2
(x+2y)/(x+y)+(2y²)/(x²-y²) x=-2 y=1/3
化简求值 (2a)/(a²-4) +1/( 2-a) a=1/2
(x+2y)/(x+y)+(2y²)/(x²-y²) x=-2 y=1/3
1/a+1/b=1/(a+b)
so (a+b)/ab=(a+b)
即(a+b)^2=ab
a^2+b^2=-ab
b/a+a/b=(b^2+a^2)/ab=-1
2.(2a)/(a²-4) +1/( 2-a)=2a/[(a+2)(a-2)]-1/(a-2)=(2a)/[(a+2)(a-2)]-(a+2)/[(a+2)(a-2)]=1/(a+2)=1/(1/2+2)=2/5
3.(x+2y)/(x+y)+(2y²)/(x²-y²)
=(x+2y)(x-y)/[(x+y)(x-y)+2y²/[(x+y)(x-y)]
=[(x+2y)(x-y)+2y²]/[(x+y)(x-y)]
=x(x+y)/[(x+y)(x-y)]
=x/(x-y)
=-2/(-2-1/3)
=6/7
so (a+b)/ab=(a+b)
即(a+b)^2=ab
a^2+b^2=-ab
b/a+a/b=(b^2+a^2)/ab=-1
2.(2a)/(a²-4) +1/( 2-a)=2a/[(a+2)(a-2)]-1/(a-2)=(2a)/[(a+2)(a-2)]-(a+2)/[(a+2)(a-2)]=1/(a+2)=1/(1/2+2)=2/5
3.(x+2y)/(x+y)+(2y²)/(x²-y²)
=(x+2y)(x-y)/[(x+y)(x-y)+2y²/[(x+y)(x-y)]
=[(x+2y)(x-y)+2y²]/[(x+y)(x-y)]
=x(x+y)/[(x+y)(x-y)]
=x/(x-y)
=-2/(-2-1/3)
=6/7
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