Rational Equations definitions Flashcards
Rational Equations definitions
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Rational Equation An equation featuring a variable in the denominator of at least one fraction, requiring special steps to solve. Denominator The bottom part of a fraction, whose value cannot be zero in rational equations to avoid undefined expressions. Restriction A value for the variable that makes the denominator zero, and therefore cannot be a valid solution. Linear Equation An equation that can be written in the form ax + b = c, often the result after clearing denominators in rational equations. Least Common Denominator The smallest expression that is a multiple of all denominators in a rational equation, used to eliminate fractions. Solution Set The collection of all values that satisfy a given equation, which may be empty if all solutions are restricted. Empty Set A set containing no elements, representing the absence of valid solutions for an equation. Fraction A numerical expression representing division, with a numerator and a denominator. Variable A symbol, often x, representing an unknown value in an equation. 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, which can be combined during simplification. Constant A fixed value in an equation, not containing any variables. Simplification The process of reducing an equation to its most basic form, often after clearing denominators and combining like terms. Numerator The top part of a fraction, representing the number being divided by the denominator. Parentheses Symbols used to group terms in an equation, indicating the order of operations.
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