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

Question

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

Answer 1

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