Let's first simplify the expression by expanding the absolute values:
|x^3 + x - 1| = |x^3 - x + 1| = x^3 + x - 1 - x^3 + x - 1 = 2x - 2
|x-1| = |x+1| = x - 1
Now substitute these values back into the original expression:
((2x - 2) - (2x - 2)) / (x-1 - (x+1))
This simplifies to:
0 / -2 = 0
So, the expression ((|x^3+x-1| - |x^3-x+1|) / (|x-1| - |x+1|)) is equal to 0 for all values of x.
Let's first simplify the expression by expanding the absolute values:
|x^3 + x - 1| = |x^3 - x + 1| = x^3 + x - 1 - x^3 + x - 1 = 2x - 2
|x-1| = |x+1| = x - 1
Now substitute these values back into the original expression:
((2x - 2) - (2x - 2)) / (x-1 - (x+1))
This simplifies to:
0 / -2 = 0
So, the expression ((|x^3+x-1| - |x^3-x+1|) / (|x-1| - |x+1|)) is equal to 0 for all values of x.