2017 AMC 8 Problems/Problem 21
Suppose , , and are nonzero real numbers, and . What are the possible value(s) for ?
There are cases to consider:
Case : of , , and are positive and the other is negative. WLOG assume that and are positive and is negative. In this case, we have that
Case : of , , and are negative and the other is positive. WLOG assume that and are negative and is positive. In this case, we have that
In both cases, we get that the given expression equals .