Given the vertical asymptotes:
[tex]x=3,x=-1,and\text{ x=0}[/tex]As we have vertical asymptotes at x = 3, x = -1, and x = 0 we have in denominator
[tex](x-3),(x+1)and\text{ }x[/tex]Hence, the rational function is
[tex]f(x)=\frac{1}{x(x-3)(x+1)}[/tex]