Question

A rational function that passes through (0,0) and (4, 8/7) has the x-axis as a horiztonal asympotote. It also has 2 vertical asymptotes x=3, x=-3.

I understand that to set it up, it is

y= ax+b / (x+3)(x-3).

I don't understand how to solve for a and b.

Put in the points. You have two points, and two unknowns.

(0,0)

0= 0+b / (0+3)(0-3).

Solving this easy: b is zero.

Now that you have b, next point
y= ax / (x+3)(x-3). ( 8/7, 8/7)
8/7= a 4
solve for a.

thank you so much for your help