for which of the following intervals does the function f(x) = (x^2-4x+3)/(x^2+x-2)(x^2-2x-3) have removable discontinuity

Question

a. [-2.5,-1.5]

b. [-1.5,-0.5]

c. [-0.5,0.5]

d. [0.5, 1.5]

e. [1.5,2.5]

Answer 1

Removable discountinuity for the rational function is where you generally have division by 0 (in which case that will be a vertical asymptote, but when factored - it will cancel out.

So factor first:

(x-3)(x-1) / (x+2)(x-1) (x-3)(x+1)

So the x-1 cancels out, and x-3 too. Discontinuity at point x=1 and at x=3

Y coordinate you will find plugin-in x=1 or x=3 into the above factored form after cancelling out

The answer is d)