Find a rational function that satisfies the given conditions:

Question

Vertical asymptotes: x=1, x=-2
X-intercept: (-5,0)

Answer 1

Vertical asymptotes: x=1, x=-2
y = 1/((x-1)(x+2))

X-intercept: (-5,0)
y = (x+5)/((x-1)(x+2))

Answer 2

Vertical asymptotes: x=1, x=-2 ---> must have had 2 denominators of the form
(x-1)(x+2)
X-intercept: (-5,0) ---> the numerator must have contained (x+5)

a possible function:
y = (x+5)/( (x-1)(x+2) )

or we could put in some constants such as
y = 7(x+5)/(3(x-1)(x+2))