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Chapter 0: Problem 14

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{x^{2}-14 x+49}{x^{2}-49}$$

Short Answer

Expert verified
The simplified expression is \((x-7)/(x+7)\) and the number to be excluded from the domain is \(-7\).

Step by step solution

01

Simplify the Rational Expression

Rewrite the numerator \(x^{2}-14x+49\) as \((x-7)^2\), and the denominator \(x^{2}-49\) as \((x-7)(x+7)\). As such, the rational expression can be rewritten as \((x-7)/(x+7)\) because one '(x-7)' term from the numerator can cancel out one '(x-7)' term from the denominator.
02

Find the Excluded Numbers

Rational expressions are undefined when the denominator equals zero. Therefore, set the denominator equal to zero and solve for x: \(x+7=0\) which gives \(x=-7\).

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$2 x^{4}\left(8 x^{4}+3 x\right)$$

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