Hello,
So I'm determining the non permissible values of the variables & for this one:
(x^2+7x+12)/(x^2-x-12)
I know the restrictions are 4<x<-3
but I can't seem to get the math to support x<-3...
I factored the denominator into
(x-4)(x+3)
x+3>0
x>-3
What am I doing wrong?
Thanks for your time! :)
You've factored correctly, but each factor is restricted to not being equal to 0. In other words, x + 3 ≠ 0, giving x ≠ -3, and x - 4 ≠ 0, giving x ≠ 4.
A little bit more tricky than that.
(x^2+7x+12)/(x^2-x-12)
= (x+3)(x+4)/( (x-4)(x+3) )
= (x+4)/(x-4) , where x ≠ -3
From what I did above, it is clear that x ≠ 4, or else I am dividing by 0 in my
final line if x = 4 , in both forms of the expression
If we graph y = (x^2+7x+12)/(x^2-x-12)
we could just as well graph y = (x+4)/(x-4)
Both graphs will have a vertical asymptote at x = 4
but we don't see a vertical asymptote at x = -3
https://www.wolframalpha.com/input/?i=Plot+y+%3D+(x%5E2%2B7x%2B12)%2F(x%5E2-x-12)
Why not??
Notice when x = -3, y = 0/0, which is indeterminate, that is,
the graph actually has a " hole" in it, namely at (-3, -1/7)
In the simplified equation the point (-3, -1/7) actually exists
https://www.wolframalpha.com/input/?i=Plot+y+%3D+(x%2B4)%2F(x-4)
You stated that the restrictions are 4<x<-3
That is false, the restrictions are x = 4 and x = -3
By saying 4<x<-3 , you are also cutting out values like x = 1.5, x = 2, x = -2 etc
4 < x < -3.
Do you mean -3 < x < 4?.
Hello! It seems like you are trying to determine the non-permissible values for a rational expression. Let's go through the steps to find the correct restrictions for the given expression.
First, we have the expression:
(x^2 + 7x + 12) / (x^2 - x - 12)
To find the non-permissible values, we need to identify the values of x that make the denominator equal to zero, since division by zero is undefined. So, let's factor the denominator:
(x^2 - x - 12) = (x - 4)(x + 3)
To find the values of x that make the denominator zero, we set each factor equal to zero and solve for x:
(x - 4) = 0 --> x = 4
(x + 3) = 0 --> x = -3
So, the factored form of the denominator tells us that x cannot equal 4 or -3, because these values would make the denominator zero.
However, in your explanation, you wrote that x + 3 > 0 implies x > -3. This is slightly incorrect. When we have x + 3 > 0, we should instead write x > -3, since adding 3 to both sides preserves the inequality. And this is indeed the correct restriction for x, because x cannot be equal to -3.
So, the correct non-permissible values for the given expression are x = 4 and x = -3. Therefore, the restrictions on x to make the expression defined are 4 < x and x < -3.
I hope this clears up any confusion. If you have any further questions, feel free to ask!