Perform the indicated operation. Simplify if possible. \[ \frac{8}{x+7}-\frac{7 x}{x^{2}-49} \] $\frac{8}{x+7}-\frac{7 x}{x^{2}-49}=\square($ Simplify your answer.)

Step 1 ：Find a common denominator for the two fractions, which is \((x+7)(x-7)\)

Step 2 ：Rewrite both fractions with the common denominator: \(\frac{8}{x+7} \cdot \frac{x-7}{x-7} - \frac{7x}{x^2-49}\)

Step 3 ：Simplify the expression: \(\frac{8(x-7)}{(x+7)(x-7)} - \frac{7x}{(x+7)(x-7)}\)

Step 4 ：Combine the fractions: \(\frac{8(x-7) - 7x}{(x+7)(x-7)}\)

Step 5 ：Simplify the numerator: \(\frac{8x-56 - 7x}{(x+7)(x-7)}\)

Step 6 ：Combine like terms: \(\frac{x-56}{(x+7)(x-7)}\)

Step 7 ：Final Answer: \(\boxed{\frac{x-56}{x^2-49}}\)