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Chapter 0: Problem 1

Find all numbers that must be excluded from the domain of each rational expression. $$\frac{7}{x-3}$$

Short Answer

Expert verified
The number that must be excluded from the domain of the expression is 3.

Step by step solution

01

Identify the denominator of the function

The denominator of the given rational expression is \(x-3\). This expression is in the denominator, so it cannot be equal to zero.
02

Solve the denominator equal to zero

To find the values that need to be excluded from the domain, solve the denominator expression equal to zero. Set up the equation:\[x - 3 = 0\] and solve for \(x\).
03

Solution for x

Adding 3 to both sides of the equation gives:[x = 3] This means, the number that must be excluded from the domain of the expression is 3

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In an inequality such as \(5 x+4<8 x-5,\) I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

This will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\).

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