1) 1/x-1 - x+2/3x^2-3x2) x+1/x-x^2 + x/x^2-13)2x^2/x-1 - 2x

Question

1) 1/x-1 - x+2/3x^2-3x
2) x+1/x-x^2 + x/x^2-1
3)2x^2/x-1 - 2x

Answer 1

1) 1/(x-1) - (x+2)/(3x²-3x)= 1/(x-1) - (x+2)/(3x(х-1))=(3х-х-2)/(3х(х-1))=2(х-1)/3х(х-1)=2/3х.
2) (x+1)/(x-x²) + x/(x²-1)=(x+1)/x(1-х) + x/(x-1)(х+1)=-(x+1)(х+1)+х²/x(x-1)(х+1)=(-х²-2х-1+х²)/(х³-х)=(-2х-1)/(х³-х)
3) 2x²/(x-1) - 2x=(2х²-2х²+2х)/(х-1)=2х/(х-1)