Problem
Which expression is equivalent to $\frac{7-x}{x^{2}-49}$ for $x \neq 7$ and $x \neq-7 ?$ $\frac{1}{x+7}$ $\frac{-1}{x+7}$ $\frac{x-7}{(x+7)(x-7)}$ $\frac{-x+7}{(x-7)(x-7)}$
Solution
Step 1 ：Factor the denominator: \(\frac{7-x}{x^{2}-49} = \frac{7-x}{(x-7)(x+7)}\)
Step 2 ：Simplify the expression: \(\frac{-(x-7)}{(x-7)(x+7)} = \boxed{\frac{-1}{x+7}}\)
