Answer
$\displaystyle \frac{x-7}{x+7}, \qquad x\neq-7, 7$
Work Step by Step
Numerator, factored:$\quad$
$x^{2}-14x+49$=$x^{2}-2\cdot x\cdot 7+6^{2}$=$\quad$... recognize a square of a difference
$=(x-7)^{2}=(x-7)(x-7)$
Denominator, factored:
$x^{2}-49$=$\quad$... recognize a difference of squares
$=(x+7)(x-7)$
Numbers to be excluded from the domain are numbers that yield 0 in the denominator:
$x\neq-7, 7$
Expression = $\displaystyle \frac{(x-7)(x-7)}{(x+7)(x-7)}$=$\qquad$... cancel $(x-7)$
= $\displaystyle \frac{x-7}{x+7}, \qquad x\neq-7, 7$
