Determine the domain of f(x). Give your answer using interval notation. f(x) = (x^2 − 25)/(2x^2 − 8x − 10)

Question

I understand that you have to factor the bottom to see what x cannot equal but how do I do that with the numerator and then write it in interval notation? 

Answer 1

you can factor the bottom first on its own:

(2x² - 8x - 10)
2(x² - 4x - 5)
2(x - 5)(x+1)

now, factor the top:
(x² - 25) 
(x + 5)(x - 5)

therefore, because of the (x - 5) on both top and bottom, x = 5 is a removable discontinuity (hole), and (x + 1) on the bottom makes an asymptote at x = -1.  both numbers are excluded from the domain.  

domain is (-infinity, -1) U (-1,5) U (5,+infinity)