Making a fraction is the easiest way to do this.
The x-intercepts give solutions to a problem that equals zero.
[tex]0 = (x-5)(x+1)[/tex]
The vertical asymptotes are values x cannot be, in a fraction the denominator can not be zero.
[tex]y = \frac{(x-5)(x+1)}{(x+4)(x-3)} [/tex]
Horizontal asymptotes are the values y approaches. This can be accomplished by making the leading term have a coefficient of 6
[tex]y = \frac{6(x-5)(x+1)}{(x+4)(x-3)} [/tex]
