#### Answer

$\dfrac{1}{x-7}$

#### Work Step by Step

Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, the given expression, $
\dfrac{x+7}{x^2-49}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x+7}{(x+7)(x-7)}
\\\\=
\dfrac{\cancel{x+7}}{(\cancel{x+7})(x-7)}
\\\\=
\dfrac{1}{x-7}
.\end{array}