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

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Answer

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

Steps

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

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