E (x)=[2x²/(4x²-4x+1)+(x-1)/(1-2x)]:[4x/(4x²-1)-1/(2x+1)]
x=R \{-1/2;1/2}
a) arătați că E (x)=(3a-1)/(2a-1) pt.x=R \{-1/2;1/2}
E (x)=[2x²/(2x-1)²+(x-1)/((1-2x)]:[(4x-2x+1)/(4x²-1)]=
{[2x²+(1-x)(2x-1)]/(2x-1)²}:[(2x+1)/(2x+1)(2x-1)]=
[(2x²-2x²+x+2x-1)/(2x-1)²]:[1/(2x-1)]=
[(3x-1)/(2x-1)²]×(2x-1)=
(3x-1)/(2x-1)
b) E (a)=(3a-1)/(2a-1)=N
1) E (a)=(a+2a-1)/(2a-1)=1+a/(2a-1)
±a=2a-1
+a=2a-1=> a=1
-a=2a-1 => -3a=-1 => a=1/3
verificarea
E (a)=1+(1/3)/(2/3-1)=1+(1/3)/(-1/3)=1-1=0 =N
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