Problem 110
Question
Explain how to find restrictions on the variable in a rational equation.
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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.
Other exercises in this chapter
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Why should restrictions on the variable in a rational equation be listed before you begin solving the equation?
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