(x^3+x)/(x(x-1)
(x(x^2+1))/(x(x-1))
(cancelx(x^2+1))/(cancelx(x-1))
(x^2+1)/(x-1)=(x^2+1)*1/(x-1)
color(green)(lim_(x->a)f(x)*g(x)=lim_(x->a)f(x) *lim_(x->a)g(x)
lim_(x->1)(x^2+1)->(1+1)=2
lim_(x->1^+)(1/(x-1))=oo
lim_(x->1^-)(1/(x-1))=-oo
lim_(x->1^+)(1/(x-1))!=lim_(x->1^-)(1/(x-1))
:.
lim_(x->1)((x^3+x)/(x(x-1)))color(white)(888)Undefined