Question

What are the coordinates of the hole in the rational function? f(x)=x2+8x−9x2−1

Answer 1

The numerator factored is $(x+9)(x-1)$
The denominator factored is $(x+1)(x-1)$
The x coordinate for the hole comes from the like factor (x - 1).
Set it equal to zero.   x - 1 = 0  so x = 1
Plug the x value into the remaining fraction $\frac{x+9}{x+1}$
$\frac{1+9}{1+1} = \frac{10}{2} =5$
The answer is (1,5)