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This problem trains for: SAT-I, AMC-8, GMAT.

How many solutions does the equation have?

First, let's make sure the fraction exists:

and apply algebraic manipulations to get:

Now, the equation branches into two equations, depending on the sign of x (note that we eliminated the value 0 from the range of x):

We solve each of the resulting equations separately, noting the range of x for each of them:

Obviously, x=0 is not allowed, so we are left with 2 solutions.