What are the coordinates of the hole in the function?

f(x)=2x^{2}−5x−12 / 3x^{2}−11x−4

Enter your answer by filling in the boxes. Enter your answer as simplified fractions, as necessary.

hole: ( , )

jjennylove Sep 6, 2019

#1**+2 **

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)

CPhill Sep 6, 2019

#4**+1 **

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.

jjennylove
Sep 6, 2019

#2**0 **

Deleted.....see Chris answer......

ElectricPavlov Sep 6, 2019

edited by
ElectricPavlov
Sep 6, 2019

edited by ElectricPavlov Sep 6, 2019

edited by ElectricPavlov Sep 6, 2019

edited by ElectricPavlov Sep 6, 2019

edited by ElectricPavlov Sep 6, 2019