4) lim x^3+3x^2-x-3
x-1 x-1
(x^3+3x^2)-x-3/x-1
x^2x+3x^2-x-3/x-1
x^2(x+3)-x+3/x-1
x^2(x+3)-(x+3)/x-1
(x^2-1)(x+3)/x-1
(x+1)(x-1)(x+3)/x-1
(x+1)(x+3)
x(x+3)+1(x+3)
x^2+3x+x+3
x^2+4x+3
1+4x+3
5+3
8
2) lim x - Koren 5 x^4-25/x^2-5
(x^2)^2-25/x^2-5
(x^2+5)(x^2-5)/x^2-5
x^2+5
(Koren 5)^2 +5
5+5
10
3) x(x+2)/x^2+5x+6
x^2+2(x)+3(x)+6
(x^2+2(x))+3(x)+6
x(x+2)+3(x+2)
(x+3)(x+2)
x(x+2)/(x+3)(x+2)
x/x+3
-2/x+3
-2/(-2)+3
-2/1
-2