For a real number x, find the number of different possible values of $\frac{|x|}{|-x|} + \frac{|-x|}{|x|}$.
Although this answer may be partially incorrect, I feel like it could help you maybe see what you have to do.
My answer is 1.
The reason for this answer is that the absolute value of x will always be x and the absolute value of -x will always be x.
So:
|x| = x
|-x| = x
Now, because all four numbers in the equation will therefore have to be equal to x, the two equations actually make:
(x / x) + (x / x)
Because any real number divided by itself is equal to 1, we now have:
1 + 1 = 2
So the answer to this equation will always be 2, therefore there is only 1 possible value for the equation.