Thread: Show work by using + and - on a number line

1. Show work by using + and - on a number line

I know how to find domains, but this instruction on the method to do it with confused me. I remember my teacher doing a long series of + and - symbols placed vertically below a number line, but I'm not sure how she did it. The problem I am supposed to find the domain of is:

2x X > 3X
_____ + _ _________
______
2 2 2
X -4 X +X-6 X + 5X + 6

Any help would be appreciated. Thanks.

2. Originally Posted by cheeseokay
I know how to find domains, but this instruction on the method to do it with confused me. I remember my teacher doing a long series of + and - symbols placed vertically below a number line, but I'm not sure how she did it. The problem I am supposed to find the domain of is:

2x X > 3X
_____ + _ _________
______
2 2 2
X -4 X +X-6 X + 5X + 6

Any help would be appreciated. Thanks.
The first thing you need to do is get that $\frac{3x}{x^2+ 5x- 6}$ on the left so you have $\frac{2x}{x^2- 4}+ \frac{x}{x^2+ x- 6}- \frac{3x}{x^2+ 5x+ 6}\ge 0$.

Now add the fractions on the left getting the common denominator. Fortunately, that's not too hard since those denominators have similar factors.
Now, determine where the numerators are 0 (that's easy: x= 0) and where the denominators are 0 (a little harder: solve that polynomial to 0 and factor it. Fortunately, you determined the factors when you formed the common denominator!

The points where the numerator or denominator are 0 separate "+" from "-". The simplest way to figure which is correct for an integerval is to look at the individual factors. An odd number of - factors, negative, and even number of - factors, positive. Also note that as you "step over" x= a, the term x- a is the only one that changes sign.

3. Thanks for the help! I did get that question right, but I have a couple more things to ask you. What did your last sentence mean? What's x=a? What's "stepping over?"