Mathematics: What are the discontinuities of the function f(x) = the quantity x squared minus 36 over the quantity 4x plus 24?

What are the discontinuities of the function f(x)

mackdoolittle1

11.03.2022

there is a point discontinuity ( hole ) at (- 6, - 3 )

factor the numerator/denominator

f(x) = $\frac{(x-6)(x+6)}{4(x+6)}$

the factor (x + 6) cancels leaving the simplified version of f(x)

f(x) = $\frac{x-6}{4}$

the removal of the factor (x + 6) from the numerator/denominator means there is a discontinuity at x + 6 = 0 , that is x = - 6

f(- 6 ) = $\frac{-6-6}{4}$ = - 3

there is a point discontinuity ( hole ) at (- 6, - 3 )

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