Let y=f(x) so we can plot using the usual x-y axes.
On the x axis mark the zeroes at -3 and 5.
Draw the asymptotes x=1 and x=4 (vertical lines). The curve will approach these two lines but will never actually touch them.
When x is very negative (much less than -3) y approaches 1 because the small constants become negligible compared to x. When x is very positive, y also approaches 1 (f(x) approaches x^2/x^2=1). Therefore y=1 is an asymptote for these large magnitude values. The smaller zero is -3, so the graph dips from the asymptote y=1 and crosses the x axis at -3 after which it starts to move towards the asymptote line x=1.
Similarly, the larger zero is where the graph dips from the asymptote y=1 for large positive values of x and cuts the x axis at x=5 and the curve draws close to the asymptote at line x=4.
Between the two asymptotes the curve assumes a narrow U shape trapped between the asymptote lines. About the midpoint between 1 and 4, about 2.5, the U has a minimum, and f(2.5)=-5.5*2.5/-(1.5*1.5)=6.1, so the point (2.5,6) is near to the minimum of this part of the graph.
Using this information a reasonable sketch of the graph can be produced.