Continuous Function Problems AP Calculus

[Loppyfoot]

Homework Statement

Let f be the function given by f(x)= (x-1)(x²-4)/ (x²-a). For What Positive Values of a is f continuous for all real numbers x?

Homework Equations

The Attempt at a Solution

What I tried doing was separating the (x²-4) into (x+2)(x-2) then moving along from there, but I can't seem to figure out what number a can be without having a discontinuity.

Thanks for trying!
Loppyfoot

 

[LCKurtz]

Hint:

1. Are polynomials continuous?
2. Are products of continuous functions continuous?
3. Are quotients of continuous continuous?

Are any of the answers above valid for all values of x or are any of them subject to some "if" conditions?

 

[Loppyfoot]

So Then, I would guess a=4, because the the (x²-4) and the (x²-4) cancel out and you are left with (x-1).

 

[LCKurtz]

You aren't permitted to cancel anything out since that makes minor changes in the function. Try answering the three questions I posed. That might lead you to the solution.