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\boxed{3v + 2}.
Solve for \( x \) in the equation \(\frac{x + 2}{x - 2} + \frac{x - 2}{x + 2} = 2\).
a = \frac{x + 2}{x - 2}, \quad \frac{x - 2}{x + 2} = \frac{1}{a}.
The equation becomes:
a + \frac{1}{a} = 2.
Multiply both sides by \( a \):
a^2 + 1 = 2a \quad \Rightarrow \quad a^2 - 2a + 1 = 0 \quad \Rightarrow \quad (a - 1)^2 = 0.
So, \( a = 1 \). Thus:
\frac{x + 2}{x - 2} = 1 \quad \Rightarrow \quad x + 2 = x - 2,
which simplifies to \( 2 = -2 \), a contradiction. This implies no solution unless we consider domain restrictions.