Problem 110
Question
Explain how to find restrictions on the variable in a rational equation.
Step-by-Step Solution
Verified Answer
To find the restrictions on the variable in a rational equation, identify the denominator(s) in the equation, set each equal to zero, and solve for the variable. These solutions are the values that the variable can not take, as they would make the denominator zero.
1Step 1: Identify the Denominator
First, the denominator of the rational equation needs to be identified. The denominator is the part of the fraction that is situated under the division line. If there is more than one fraction in the equation, there may be more than one denominator.
2Step 2: Set the Denominator Equal to Zero
Secondly, write down a new equation where the denominator is set equal to zero. This is done because the values of the variable that would make the denominator zero are the values that are not allowed, as division by zero is undefined.
3Step 3: Solve for the Variable
Thirdly, solve the equation set up in the previous step. The solutions to this equation are the restrictions for the variable.
Other exercises in this chapter
Problem 108
Solve each equation in Exercises \(83-108\) by the method of your choice. $$\frac{3}{x-3}+\frac{5}{x-4}=\frac{x^{2}-20}{x^{2}-7 x+12}$$
View solution Problem 109
Suppose you are an algebra teacher grading the following solution on an examination: $$ \begin{array}{c} -3(x-6)=2-x \\ -3 x-18=2-x \\ -2 x-18=2 \\ -2 x=-16 \\
View solution Problem 111
Why should restrictions on the variable in a rational equation be listed before you begin solving the equation?
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For each planet in our solar system, its year is the time it takes the planet to revolve once around the sun. The formula $$E-0.2 x^{\frac{3}{2}}$$ models the n
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