What are the vertical horizontal asymptotes x intercept and

What are the vertical, horizontal asymptotes, x intercept, and y intercept of the function r(x) = (x+2) / (x^2 - 4x - 5)

r(x) = (x+2)/(x^2 - 4x - 5)

r(x) = (x+2)/((x - 5)(x+1))

vertical asymptotes =>

denominator =0

x-5=0 , x+1=0

x =5 , x =-1

horizontal asymptote =>

y =lim_x-> (x+2)/((x - 5)(x+1))

y =lim_x-> x(1+(2/x))/(x²(1 - (5/x))(1+(1/x)))

y =lim_x-> (1+(2/x))/(x(1 - (5/x))(1+(1/x)))

y=(1+0)/((1-0)(1+0))

y =1/

y =0 is horizontal asymptote

x intercept:

r(x)=0

(x+2)/(x^2 - 4x - 5)=0

x+2=0

x=-2

x intercept (-2,0)

y intercept:

x =0

y=(0+2)/(0^2 - 4*0 - 5)

y =-2/5

y intercept (0,-2/5)