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Chapter 0: Problem 3

Find all numbers that must be excluded from the domain of each rational expression. $$\frac{x+5}{x^{2}-25}$$

Short Answer

Expert verified
The values that need to be excluded from the domain of the given rational expression are \(x = 5\) and \(x = -5\).

Step by step solution

01

Identify the denominator of the rational expression

The denominator of the given rational expression is \(x^{2}-25\).
02

Set the denominator equal to zero

To find the values that need to be excluded from the domain, we need to set the denominator equal to zero and solve for x. So our equation is \(x^{2} - 25 = 0\).
03

Solve for x

By factorizing the equation we get \((x - 5)(x + 5) = 0\). Setting each term equal to zero gives us two solutions, \(x = 5\) and \(x = -5\). These are the values that make the denominator zero.

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