Rational Equations definitions Flashcards
Rational Equations definitions
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Rational Equation An equation containing variables in the denominator of one or more fractions, requiring special steps to solve. Denominator The bottom part of a fraction, whose value cannot be zero in rational equations. Restriction A value for a variable that would make a denominator zero, and thus is excluded from possible solutions. Least Common Denominator The smallest expression that is a common multiple of all denominators in a rational equation. Linear Equation An equation of the first degree, often resulting from clearing denominators in a rational equation. Solution Set The collection of all values that satisfy a given equation, possibly empty if restrictions are violated. Empty Set A set containing no elements, representing no valid solutions for an equation. Fraction A numerical quantity expressed as one number divided by another, often present in rational equations. Variable A symbol, typically x, representing an unknown value in an equation. Constant A fixed value in an equation, not affected by the variable. Distribution The process of multiplying a term across terms inside parentheses, used when clearing denominators. Like Terms Terms in an equation that have the same variable raised to the same power and can be combined. Isolating x The process of rearranging an equation to have the variable x alone on one side. Parenthesis Symbols used to group terms, especially important when distributing or combining terms. Numerator The top part of a fraction, representing the number being divided by the denominator.
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