Factorise the denominator. The function will be continuous everywhere except where the denominator is 0.
So your question really is "How do I factor ?" It would have been better to say that in your first post.
"x" is an obvious factor: . Now the only possible zeros of are 1, -1, 7, and -7 (because if it were to factor as (x-a)(x-b)(x-c) the last term would be abc=-7- and the only integer factors of 7 are 1 and 7). Trying x= 1 in the polynomial we get . That tells us that x- 1 is also a factor. Dividing by x- 1 leaves which has discriminant ( ) equal to so there are no more real number zeros of the polynomial. .