Enhance Your Learning with Rational Expressions and Equations Flash Cards for quick understanding
An expression that can be written as a ratio of two polynomials, where the denominator is not equal to zero.
An equation that contains one or more rational expressions.
To reduce a rational expression to its simplest form by canceling common factors.
A shared multiple of the denominators of two or more rational expressions.
To multiply two or more rational expressions, multiply the numerators together and the denominators together.
To divide two rational expressions, multiply the first expression by the reciprocal of the second expression.
To add two or more rational expressions with the same denominator, add the numerators together and keep the common denominator.
To subtract two or more rational expressions with the same denominator, subtract the numerators and keep the common denominator.
To solve a rational equation, find the values of the variable that make the equation true.
A solution that does not satisfy the original equation after substitution.
Real-world problems that can be modeled and solved using rational expressions.
To graph a rational function, determine the vertical asymptotes, horizontal asymptotes, and points of discontinuity.
A vertical line that the graph of a rational function approaches but never crosses.
A horizontal line that the graph of a rational function approaches as the input values become very large or very small.
An inequality that contains one or more rational expressions.
To solve a rational inequality, find the values of the variable that make the inequality true.
A method used to decompose a rational expression into simpler fractions.
A rational expression that contains one or more rational expressions in the numerator, denominator, or both.
A fraction that contains one or more fractions in the numerator, denominator, or both.
The set of all possible input values for a function or expression.
The set of all possible output values for a function or expression.
A test used to determine if a graph represents a function.
A relationship between two variables where the product of the variables is a constant.
A relationship between two variables where the ratio of the variables is a constant.
A line that a graph approaches but never crosses.
A point where a function is undefined or has a jump, hole, or vertical asymptote.
A function that can be written as the ratio of two polynomials, where the denominator is not equal to zero.
An expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and non-negative integer exponents.
The top part of a fraction or rational expression.
The bottom part of a fraction or rational expression.
A number or expression that divides another number or expression without leaving a remainder.
To remove common factors from the numerator and denominator of a fraction or rational expression.
The multiplicative inverse of a number or expression.
An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
An equation of the form ax + b = 0, where a and b are constants and a ≠ 0.
A number that represents the power to which a base is raised.
A symbol used to represent a quantity that can change or vary.
A number or symbol multiplied by a variable or variables in a term.
A combination of numbers, variables, and operations, without an equal sign.
A mathematical statement that two expressions are equal.
A mathematical statement that two expressions are not equal.
A value or values that make an equation or inequality true.
A term that contains a variable.
A term that does not contain a variable.
Terms that have the same variable(s) raised to the same power(s).
Terms that have different variable(s) or different power(s) of the same variable(s).
A number, variable, or product or quotient of numbers and variables.