Evaluate rational expressions Set 1

Learning Objectives Define a rational expression and identify its components. Determine the values for which a rational expression is undefined by setting the denominator to zero. Substitute given numerical values for variables within a rational expression. Apply the correct order of operations (PEMDAS/BODMAS) to evaluate the numerator and denominator separately. Simplify the resulting numerical fraction to its lowest terms. Evaluate rational expressions that contain multiple variables. Ever wondered how engineers calculate the stress on a bridge support or how economists model average cost? 🌉 They often use rational expressions! This tutorial introduces the fundamental skill of evaluating rational expressions. You will learn how to substitute numerical values into these a...

TermDefinitionExample Rational ExpressionAn expression that can be written as a fraction P/Q, where P and Q are polynomials and the denominator Q is not the zero polynomial.The expression (x^2 + 5x + 6) / (x + 2) is a rational expression. VariableA symbol, typically a letter like x or y, that represents an unknown numerical value.In the expression (3y - 1) / (y^2), 'y' is the variable. SubstitutionThe process of replacing variables in an expression with their given numerical values.To evaluate (a + 7) / 2 for a = 5, we substitute 5 for 'a' to get (5 + 7) / 2. EvaluationThe process of finding the single numerical value of an expression after substitution has been performed.The evaluation of (5 + 7) / 2 results in 12 / 2, which simplifies to 6. DomainThe set of all possi...

The Evaluation Principle To evaluate a rational expression R(x) = P(x) / Q(x) at x = a, calculate R(a) = P(a) / Q(a). This is the primary process for evaluation. Substitute the given value 'a' for every instance of the variable 'x' in both the numerator and the denominator, then simplify. The Undefined Condition A rational expression R(x) = P(x) / Q(x) is undefined for any value 'a' where Q(a) = 0. Before evaluating, it's a good practice to check if the given value for the variable makes the denominator zero. If it does, the expression is undefined, and no further calculation is needed. Order of Operations (PEMDAS) 1. Parentheses 2. Exponents 3. Multiplication & Division (L to R) 4. Addition & Subtraction (L to R) This st...