Answered

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 )

Verified Answer :

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)

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