Can you solve this math problem?

Question

vera_ewing · Answer

What value is a discontinuity of $$\frac{ x^2+3x-4 }{ x^2+x-12 }$$

k_lynn · Answer

Hmm.  Maybe @iGreen or @inowalst can help you with this one.

vera_ewing · Answer

@campbell_st It's x = -2 right?

inowalst · Answer

I'm not sure its -2..

vera_ewing · Answer

Oh... maybe -4?

campbell_st · Answer

check the factoring of the denominator.. factors of -12 that add to 1...

vera_ewing · Answer

So when I do that I get -2 @campbell_st Is that the right answer?

campbell_st · Answer

well factor of -12 than the larger factor is positive to get 1... the smaller factor is negative

12 x -1    6 x -2    and 4 x -3 

which pair add to 1


-2 isn't correct...

vera_ewing · Answer

@campbell_st So it's actually -1?

campbell_st · Answer

no, look at the 3 pairs of factors I have you, they all multiply to -12... find the pair that adds to 1...

vera_ewing · Answer

4x-3 adds to 1 right?

campbell_st · Answer

correct... so the fraction can be written as 

$$\frac{x^2 + 3x - 4}{(x +4)(x -3)}$$

now factor the numerator and thn remove the common factor

vera_ewing · Answer

@campbell_st  so that would make the answer x = -3 right??

campbell_st · Answer

no.... still not right... what does the numerator factor to..?

vera_ewing · Answer

1?

campbell_st · Answer

no... can you factor the numerator...?

vera_ewing · Answer

ohh wait the answer is -4. thanks for helping me understand! :)

campbell_st · Answer

again, no that is not the answer

vera_ewing · Answer

are you kidding me? it has to be -4 though

campbell_st · Answer

just factor the numerator...

vera_ewing · Answer

i'm not sure how to. how do you do that?

campbell_st · Answer

I know how to do it.... you can find the factors of -4 that add to 3...?

then it would be 

$$x^2 + 3x - 4 = (x + factor ~1)(x + factor~2)$$

vera_ewing · Answer

(x+4)(x+3) ??

campbell_st · Answer

no, that would result in a constant of 12 and the coefficient of x being 7

campbell_st · Answer

its a really difficult  question if you can't factor quadratics....

vera_ewing · Answer

I'm so confused...what would the answer be? It has to be either x=-1, x=-2, x=-3, or x=-4 and you said those are wrong

campbell_st · Answer

ok so the fraction in factored form is$$\frac{(x +4)(x -1)}{(x+4)(x -3)}$$

vera_ewing · Answer

ok...

campbell_st · Answer

no it depends on which discontinuities you need to identify... asymptotes or points or both

campbell_st · Answer

I'm in Australia... and need to know point discontinuities....its the value of x that makes the common factor zero

campbell_st · Answer

the asymptote, which is the more common discontinuity, the the value of x that makes the denominator zero after the common factor is removed  $$\frac{x -1}{x -3}$$

campbell_st · Answer

hope it makes sense....but realistically, you can't do these questions with being able to factor quadratics

vera_ewing · Answer

But I still have no idea what the answer is...Can you please tell me?