What value is a discontinuity of

Question

vera_ewing · Answer

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

igreen · Answer

Hmm..I don't think so.

igreen · Answer

Not sure how to do this.

thesmartone · Answer

First factor the denominator and then set it equal to 0. Whatever you get for x is the discontinuity of the graph.

vera_ewing · Answer

(x+4)(x-3) is the denominator after I factor it right?

thesmartone · Answer

Yup, and set it equal to 0.

So:
$\sf (x+4)(x-3)=0$

vera_ewing · Answer

x^2 - 3x + 4x - 12

thesmartone · Answer

Actually, no.

$\sf (x+4)(x-3)=0$

$\sf (x+4)=0$
$\sf (x-3)=0$

And we have two answers :P

vera_ewing · Answer

A. x = -4
	B. x = -2
	C. x = -3
	D. x = -1

vera_ewing · Answer

Which one is it?

thesmartone · Answer

x+4=0
x-3=0

solve both equations for x. Which ever one has the answer choice is your answer.
Since these 2 equations have either 3, or 4 in it, we can eliminate B and D.

vera_ewing · Answer

Oops I mean -4 and 3

vera_ewing · Answer

So is the answer C?

thesmartone · Answer

$\sf x-3=0$
$\sf x-3+3=0+3$
$\sf x=3$

thesmartone · Answer

Notice it is positive 3 not negative 3.

vera_ewing · Answer

That's weird. So what's the answer?

thesmartone · Answer

We still have another equation, solve for x.

$\sf x+4=0$

thesmartone · Answer

subtract 4 on both sides... and since I told you C was wrong and that we could eliminate B and D... there is only one possible answer .-.

thesmartone · Answer

@vera_ewing