You can put this solution on YOUR website! here is the answer
the vertical asymptote is x=2 because 2 makes the denominator zero
the zeros of the given rational function is 1 and -3
here is the way
x^2+2x-3 over x-2=0
x^2+2x-3=0
x^2+3x-x-3=0
x(x+3)-1(x+3)=0
(x+3)(x-1)=0
x+3=0 or x-1=0
x=-3 or x=1
i hope you will be satisfied