5) \( \frac{x+7}{x^{2}-7^{2}}= \)

To simplify \( \frac{x+7}{x^{2}-7^{2}} \), we first recognize that the denominator can be factored using the difference of squares formula \( a^2 - b^2 = (a-b)(a+b) \). Therefore, we can rewrite it as: \[ x^{2} - 7^{2} = (x - 7)(x + 7) \] Now substituting this into the equation gives us: \[ \frac{x+7}{(x - 7)(x + 7)} \] Notice that the \( x + 7 \) terms in the numerator and denominator can be canceled, provided \( x \neq -7 \): \[ \frac{1}{x - 7} \quad \text{for } x \neq -7 \] So the simplified expression is: \[ \frac{1}{x - 7} \quad \text{(where } x \neq -7\text{)} \]