Question

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

( -1, 8 )


( -1, 4)


( 1, 5 )


( 1, 4 )

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
`(x+9)/(x+1)`

`(1+9)/(1+1) = (10)/(2) =5`
The answer is (1,5)