Solving Quadratic Equations Involving Fractions (Leaving Cert Mathematics): Flashcards
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What are quadratic equations involving fractions?
What are quadratic equations involving fractions?
Equations with algebraic fractions (variables in denominators) that lead to quadratics when solved
What are rational equations?
What are rational equations?
Another name for quadratic equations involving fractions
Key technique for solving rational equations
Key technique for solving rational equations
Multiply every term by the LCM of all denominators
What does the LCM method achieve?
What does the LCM method achieve?
Eliminates fractions from the equation
First step in solving rational equations
First step in solving rational equations
Identify all denominators
Second step in solving rational equations
Second step in solving rational equations
Find the LCM of denominators
Third step in solving rational equations
Third step in solving rational equations
Multiply every term by the LCM
Methods to solve the resulting quadratic
Methods to solve the resulting quadratic
Factorising or using the quadratic formula
Essential check after solving
Essential check after solving
Substitute solutions back into original equation
What values cannot be solutions?
What values cannot be solutions?
Values that make any denominator equal to zero
Common mistake with the LCM method
Common mistake with the LCM method
Forgetting to multiply ALL terms by the LCM
Result after applying LCM method
Result after applying LCM method
Always a quadratic equation