SOLUTION: Absolute Value Expression: |x+2| divided by x+2 Answer is: 1 for x>-2; undefined for x=-2; -1 for x<-2 Can you explain the steps for this expression?

Question 644731: Absolute Value Expression:
|x+2| divided by x+2
Answer is: 1 for x>-2; undefined for x=-2; -1 for x<-2
Can you explain the steps for this expression?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If x > -2, then we can add 2 to both sides to get x + 2 > 0

So the expression x+2 is positive in this case.

So |x+2| = x+2 in this case as well (since the absolute value doesn't change a positive number)

This means |x+2|/(x+2) = (x+2)/(x+2) = 1 when x > -2

So |x+2|/(x+2) = 1 when x > -2

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It's undefined for x = -2 since plugging this value into the expression yields a 0 in the denominator (you can't divide by zero)

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When x < -2, then x+2 < 0 which means |x+2| = -(x+2)

So |x+2|/(x+2) = -(x+2)/(x+2) = -1 when x < -2

which means |x+2|/(x+2) = -1 when x < -2

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