I'm having some trouble understanding this.
If x<-2, then |x+2|/x+2= -x+2/x+2= -x/x= -1, right? <----you got the right answer, but for the WRONG reason.....
If x < -2, then x + 2 < 0. By the definition of absolute value, if a < 0, | a | = -a. So, if (x + 2) < 0, then | x + 2 | = - (x + 2).....NOT -x + 2 as you've indicated. And you cannot simplify (-x + 2) / (x + 2) by dividing out the 2s to get -x/x.........
If x < -2, | x + 2 | / (x + 2) = -(x + 2) / (x + 2), which is -1 (because (x + 2)/(x + 2) = 1)
But what if x<-1? Could someone show me how this breaks down when x is less than negative 1?
The problem is written like this:
|x+2|/x+2, x< -2
What I'm wondering is how it breaks down if:
|x+2|/x+2, x< -1
If x < -1, you have three possibilities to consider...
If x = -2 (which could happen if x < -1), then the fraction is undefined because the denominator is 0.
If -2 < x < -1, (x + 2) is non-negative. When a > 0, | a | = a, so when x + 2 is non-negative, | x + 2 | = x + 2, and your fraction becomes (x + 2)/(x + 2), or 1.
If x < -2, (which would be part of the domain x < -1), as we've seen above, |x + 2| / (x + 2) = -1
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You could help me out further by breaking down this:
|x-1|/ x-1, x> 0
This is similar to your second question above...you need to consider three possibilities....
If 0 < x < 1, (x - 1) is negative....so |x - 1| = -(x - 1) and you should be able to figure out the value of the fraction |x - 1| / (x - 1)
If x = 1, the fraction is undefined (because the denominator will have a value of 0).
If x > 1, (x - 1) is positive...and |x - 1| = x - 1. Again, you should be able to figure out the value of the fraction in this case.