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Chapter 1: Problem 110

Explain how to find restrictions on the variable in a rational equation.

Short Answer

Expert verified
To find restrictions on a variable in a rational equation, identify the rational expressions in the equation, set their denominators equal to zero and solve for the variable. These solutions are the restrictions for the variable as they would cause the denominator to be zero, thereby making the rational equation undefined.

Step by step solution

01

Identify and isolate the rational expressions

Locate the fractions whose numerators or denominators are polynomials in the equation. This might also involve first simplifying the given equation where necessary.
02

Set the denominator equal to zero

For each fraction, set the denominator equal to zero and solve for the variable. This is due to the nature of mathematical operations, specifically division. Division by zero is undefined, meaning that that particular value of the variable is invalid or a restriction.
03

Combine the separate restrictions

From each fraction derived, gather all values obtained for the variable and combine them. These are all the values that the variable in the equation cannot take. These are the restrictions on the variable.

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