Solving Rational Equations
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a rational equation?
Back
A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and denominator are polynomials.
2.
FLASHCARD QUESTION
Front
What are the domain restrictions for rational equations?
Back
The domain restrictions for rational equations are the values of the variable that make the denominator equal to zero, as these values are not allowed.
3.
FLASHCARD QUESTION
Front
State the domain restrictions for the equation \( \frac{1}{x-2} \).
Back
x ≠ 2.
4.
FLASHCARD QUESTION
Front
How do you solve a rational equation?
Back
To solve a rational equation, find a common denominator, eliminate the denominators by multiplying both sides by it, and then solve the resulting equation.
5.
FLASHCARD QUESTION
Front
What is the first step in solving \( \frac{1}{x-2} = \frac{3}{x+1} \)?
Back
Identify the common denominator, which is (x-2)(x+1).
6.
FLASHCARD QUESTION
Front
What does it mean to check for extraneous solutions?
Back
Checking for extraneous solutions means verifying that the solutions obtained do not make any denominator in the original equation equal to zero.
7.
FLASHCARD QUESTION
Front
Solve the rational equation: \( \frac{2}{x+3} = \frac{4}{x-1} \).
Back
Cross-multiply to get: 2(x-1) = 4(x+3). Solve to find x = -5.
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