+1995 What are the coordinates of the hole in the function?
f(x)=2x2−5x−12 / 3x2−11x−4
Enter your answer by filling in the boxes. Enter your answer as simplified fractions, as necessary.
hole: ( , )
+129852 f(x) = (2x^2 - 5x - 12) / ( 3x^2 -11x - 4)
Factor the top/bottom ......one thing that might make this easier is to note that we probably have like linear factors on top/bottom
(2x^2 - 5x - 12) ( 2x + 3) ( x - 4) (2x + 3)
_____________ = ______________ = _______ (1)
3x^2 - 11x - 4 (3x + 1)( x - 4) (3x + 1)
The x value where the "hole" occurs where the like linear factors = 0 .....so....
x - 4 = 0
x = 4
The y value of the coordinate is found by putting the x value into (1) = [ 2(4)+3] / [ 3(4) + 1] = 11/ 13
So....the "hole" is at (4, 11/13)
+1995 I forgot to include my answer, but that is what I had wrote for the answer. Awesome! Just wanted to double check my answer 
. Gonna make some more notes of your explnatation ,thanks.
+37146 Deleted.....see Chris answer......
