We are asked to find the value of $(f \circ g)'$ at $x = 49$, where the functions are defined as follows:

$f(u) = \frac{u - 1}{u + 1}, \quad u = g(x), \quad x = 49.$

To approach this, we need to apply the chain rule, which states that:

$(f \circ g)'(x) = f'(g(x)) \cdot g'(x).$

However, the function $g(x)$ is not fully specified in the problem. Could you provide the exact form of $g(x)$? Without it, I won't be able to compute the derivatives of $f$ and $g$.

Let me know, and I'll guide you through the rest of the solution once I have that information!