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The given function is:

\[
f(x) = \frac{x}{x^2 - 49}
\]

### Steps to analyze the function:

1. **Simplify the denominator**: Notice that the denominator \( x^2 - 49 \) can be factored using the difference of squares:
   \[
   x^2 - 49 = (x - 7)(x + 7)
   \]
   So, the function can be rewritten as:
   \[
   f(x) = \frac{x}{(x - 7)(x + 7)}
   \]

2. **

Learn how to factorize and simplify the rational function f(x) = x / (x^2 - 49). This problem explores key algebraic concepts such as rational functions and the difference of squares, with a detailed step-by-step solution. Suitable for students in Grades 9-11.

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