find the sum of p+m if the function

Question

g(x)= p(x^2-m)/(x+2)(x+5)has a horizontal asymptote at y=5 and a hole at x=-2

Answer 1

we know that at large x,

g(x) =~ 5, so p = 5, giving us

g(x) = 5(x^2 - m)/(x+2)(x+5)
A hole at x = -2 means that the numerator is divisible by (x+2) so that

g(x) = 5(x+2)(x-2)/(x+2)(x+5)
making m = 4

p+m = 9