Hobbs Lane
08/06/2023 · Middle School
The following rational equation has denominators that contain variables. For this equation, a. Write the value or va are the restrictions on the variable. beeping the restrictions in mind, solve the equation. a. What is/are the value or values of the variable that make(s) the denominators zero? (Simplify your answer. Use a comma to separate answers as needed.)
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Step-by-step Solution
To provide a complete answer, I need the specific rational equation you're referring to. However, I can guide you on how to find the restrictions on the variable in a rational equation.
1. **Identify the Denominators**: Look at the denominators of the rational equation.
2. **Set Denominators to Zero**: For each denominator, set it equal to zero and solve for the variable. This will give you the values that make the denominators zero.
3. **List the Restrictions**: The values you find are the restrictions on the variable, meaning the variable cannot take these values in order for the equation to be defined.
For example, if you have a rational equation like:
\[
\frac{1}{x-3} + \frac{2}{x+5} = 0
\]
You would set the denominators to zero:
1. \(x - 3 = 0 \Rightarrow x = 3\)
2. \(x + 5 = 0 \Rightarrow x = -5\)
Thus, the restrictions on the variable \(x\) would be \(x \neq 3, x \neq -5\).
If you provide the specific rational equation, I can help you find the restrictions and solve the equation.
Quick Answer
Identify the denominators, set them to zero, and solve for the variable to find the restrictions.
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