what are the coordinates of the hole in the graph of the function?

The answer to your question is: (5/2, -6)

Step-by-step explanation:

Given    f(x) = (6x - 36) / (2x² - 17x + 30)

Factorize both, numerator and denominator

Numerator = 6(x - 6)

Denominator =    2x² - 12x - 5x + 30

                      =   2x(x - 6) - 5(x - 6)

                      = (x - 6) (2x - 5)

Now     f(x) = 6(x - 6) / (x - 6) (2x - 5)     Cancel (x - 6)

            f(x) = 6 / 2x - 5

Find the hole           2x - 5 = 0

                                2x = 5

                                x = 5/2

In 5/2 there is a hole, in y is approximately -6

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

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