Which expression is equivalent to $\frac{7-x}{x^{2}-49}$ for $x \neq 7$ and $x \neq-7 ?$
$\frac{1}{x+7}$
$\frac{-1}{x+7}$
$\frac{x-7}{(x+7)(x-7)}$
$\frac{-x+7}{(x-7)(x-7)}$

Answer

Expert–verified

Hide Steps

Answer

Simplify the expression: $\frac{-(x-7)}{(x-7)(x+7)} = \boxed{\frac{-1}{x+7}}$

Steps

Step 1 ：Factor the denominator: $\frac{7-x}{x^{2}-49} = \frac{7-x}{(x-7)(x+7)}$

Step 2 ：Simplify the expression: $\frac{-(x-7)}{(x-7)(x+7)} = \boxed{\frac{-1}{x+7}}$