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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 numbers that must be excluded from the domain of the given rational expression are \(x = -5\) and \(x = 5\).

Step by step solution

01

Identify the denominator

Firstly, identify the denominator of the fraction which is \(x^{2}-25\)
02

Set the denominator equal to zero

In order to find the values making this zero, set the denominator equal to zero and solve: \(x^{2}-25 = 0\)
03

Solve the equation

This equation can be factored using the difference of squares: \(x^{2}-5^{2} = 0\), so \((x+5)(x-5) = 0\). Setting each factor equal to zero and solving for \(x\), we get \(x = -5\) and \(x = 5\).
04

Identify the numbers to be excluded

The numbers that must be excluded from the domain are therefore \(x = -5\) and \(x = 5\), because these values would make the denominator equal to zero.

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