Simplify f(x). f(x) = (x2 - x - 6)/(x2 - 2x - 3)

Question

I got the simplification correct which is: f(x) = x+2 x+1?  but I couldn't get for x ≠____. 

I tried -3/2 and -1 and they were both incorrect. I though it meant to put where x cannot equal zero. Can someone please help??

Answer 1

Let's factor the numerator:   (x^2 - x - 6) = (x -3)(x + 2)     [check this using FOIL]

Then, the denominator:  (x^2 - 2x -3) = (x - 3)(x + 1)         [also check]

 

Now, notice that both the numerator and denominator have (x-3) as a factor and can be cancelled.  This is (x+2)/(x+1).  However, since the problem has the denominator expressed the way it does, and it can be factored into two terms, neither of them can be 0 (because that makes the ratio undefined).  So, x ≠ 3 and x ≠ -1 (these make the factors 0 and the denominator will be 0 -- not allowed).