Why can't you simplify Ix-1I / (x-1). What exactly does the absolute value mean in this case?

Answer 1

Everything inside | | is positive.

x can not equal 1 as the bottom will be zero.
When x is positive, except for 1, the answer is 1.
When x is below zero, or negative, the answer is -1.

Answer 2

Well let's take a look at the cases. If X is a real number, it can be positive, negative, or 0

If X is positive, then |x-1| / (x-1) = 1
If X is negative, then |x-1| / (x-1) = -1
If X is 0, then -1

The absolute value causes the answer to that equation to be broken up into 2 intervals.

Answer 3

using the positive value
( x-1 ) / ( x-1 ) = 1

using the negative value
- ( x-1 ) / ( x-1 ) = -1

Answer 4

What exactly does the absolute value mean in this case?

the same thing it means in any case