Solving Rational Equations

Flashcard
•
Mathematics
•
9th - 12th Grade
•
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 domain restrictions in rational equations?
Back
Domain restrictions are values of the variable that make the denominator zero, which are not allowed in rational equations.
3.
FLASHCARD QUESTION
Front
State the domain restrictions for the rational 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 domain restrictions: x ≠ 2 and x ≠ -1.
6.
FLASHCARD QUESTION
Front
What does it mean to cross-multiply in rational equations?
Back
Cross-multiplying means multiplying the numerator of one fraction by the denominator of the other fraction to eliminate the fractions.
7.
FLASHCARD QUESTION
Front
Solve the equation \( \frac{2}{x+3} = \frac{4}{x-1} \).
Back
Cross-multiply to get 2(x-1) = 4(x+3). Simplifying gives x = -5.
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