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For a real number x, find the number of different possible values of $\frac{|x|}{|-x|} + \frac{|-x|}{|x|}$.

 Apr 26, 2021
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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 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.

 Apr 26, 2021

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