What value is a discontinuity of x squared plus 8 x plus 4, all over x squared minus x minus 6?

Question

hero · Answer

You are given $$\frac{x^2 + 8x + 4}{x^2 - x - 6}$$ and asked to find the value of the discontinuity, correct?

anonymous · Answer

yes

anonymous · Answer

-1 -3 -3 or -2

anonymous · Answer

how do you find the discontinuity

hero · Answer

The discontinuity of the rational expression occurs where the numerator and denominator has common factors, correct?

anonymous · Answer

Sure.

anonymous · Answer

So its -2

hero · Answer

And if we factor the rational expression completely we should be able to find those common expressions right?

anonymous · Answer

Hmm, yes.

hero · Answer

How did you arrive at -2? Would you mind explaining?

hero · Answer

Because $x^2 + 8x + 4$ doesn't appear to be factorable. Did you make a mistake while posting the expression?

anonymous · Answer

Because it goes into 8 and 4?

hero · Answer

-2 is correct, however, that's not the reason why.

hero · Answer

$x^2 + 8x + 4$ factors, just not over integers. 

Observe that 

$\dfrac{x^2 + 8x + 4}{x^2 - x - 6} $ factors to $\dfrac{(x - 2(\sqrt{3}-2))(x + 2(\sqrt{3}  +2))}{(x - 3)(x + 2)}$