# Chapter P - Section P.6 - Rational Expressions - Exercise Set - Page 84: 14

$\displaystyle \frac{x-7}{x+7}, \qquad x\neq-7, 7$

#### 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 $(x-7)$ = $\displaystyle \frac{x-7}{x+7}, \qquad x\neq-7, 7$

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