use limits to find and verify all asymptotes in the graph y= sqr root (5+x^2)/(3-x)

where do you get stuck?

You know that:
vertical asymptotes occur where the denominator is zero.
horizontal asymptotes occure when the degree of the numerator is the same or less than that of the denominator
slant asymptotes occur when the degree of the top is one more than the bottom's