Wykonaj dodawanie ,odpowiedz podaj w najprostszej postaci.
a) 2/x^2+x + 2/x^2-x
b) 1/x^2-1 + 1/x^2+2x+1
1.a) 2/x^2+x + 2/x^2-x=2(x^2-x)+2(x^2+x)/(x^2+x)(x^2-x)=2x^2-2x+2x^2+2x/x^4-x^2=
=4x^2/x^2(x^2-1)=4/x^2-1 ; Dwyr=R-{-1,0,1}
1.b) 1/x^2-1 + 1/x^2+2x+1=1/(x-1)(x+1) + 1/(x+1)(x+1)=x+1+x-1/x+1=2x/x+1 ;
Dwyr=R-{-1,1}
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1.a) 2/x^2+x + 2/x^2-x=2(x^2-x)+2(x^2+x)/(x^2+x)(x^2-x)=2x^2-2x+2x^2+2x/x^4-x^2=
=4x^2/x^2(x^2-1)=4/x^2-1 ; Dwyr=R-{-1,0,1}
1.b) 1/x^2-1 + 1/x^2+2x+1=1/(x-1)(x+1) + 1/(x+1)(x+1)=x+1+x-1/x+1=2x/x+1 ;
Dwyr=R-{-1,1}