Algebra II - Rational Expressions | Mathematics

Preview (10 of 107 Pages)

100%

Algebra II - Rational Expressions - Page 1 preview image

Loading page ...

Study GuideAlgebra II–RaƟonal Expressions1. Examples of RaƟonal ExpressionsArational expressionis simply another way of writing afraction. Just like regular fractions, itrepresentsdivision.In a fraction, thenumerator(top part) is divided by thedenominator(bottom part).For example:meansa divided by b.Rational Expressions with PolynomialsIn algebra, rational expressions often containpolynomialsin the numerator, the denominator, orboth.This can make them look more complicated than regular fractions, but the main idea is still the same:one expression is being divided by another.Sometimes the numerator or denominator maycontainmore complex algebraic expressions, which requires extra steps to simplify.Definition of a Rational ExpressionArational expressionis thequotient (division) of two polynomials.It has the form:where:•(P(x)) is a polynomial (numerator)•(Q(x)) is a polynomial (denominator)•(Q(x)≠0)The denominatorcannot be zero, because division by zero is undefined.

Algebra II - Rational Expressions - Page 2 preview image

Loading page ...

Study GuideExamples of Rational ExpressionsHere are some examples:In each example, one expression is divided by another.Whole Numbers as Rational ExpressionsEven expressions that look likewhole numbers or polynomialscan be written as rationalexpressions.For example:can be written as:Since1 is a polynomial, this expression still fits the definition of a rational expression.Complex Rational ExpressionsSometimes rational expressions may containfractions inside other fractions.These are calledcomplex rational expressions.

Algebra II - Rational Expressions - Page 3 preview image

Loading page ...

Study GuideThey may require extra steps to simplify, such as:•finding common denominators•simplifying fractions•factoring polynomialsYou will learn more about these techniques later.Summary•Arational expressionis a fraction that containspolynomials.•It representsdivision of two polynomials.•The denominatorcannot equal zero.•Rational expressions can look like:oregular fractionsoalgebraic fractionsopolynomials written over 1Examples:Even expressions likecan be written asso they are also rational expressions.

Algebra II - Rational Expressions - Page 4 preview image

Loading page ...

Study Guide2. Quiz: Examples of RaƟonal Expressions1. QuestionRewrite the expression as a fraction:(5a + 3b) ÷ 7cAnswer Choices•((8ab)/7c))•(7c/(5a + 3b))•((5a + 3b)/7c))Correct Answer((5a + 3b)/7c))Why This Is CorrectDivision can be written as a fraction.So the numerator is5a + 3band the denominator is7c.2. QuestionRewrite the expression as a fraction:19x ÷ (5x²−3x + 2)Answer Choices•(19x/(5x2-3x + 2))•((5x2-3x + 2)/19x))•(19/(5x–1))

Algebra II - Rational Expressions - Page 5 preview image

Loading page ...

Study GuideCorrect Answer(19x/5x2-3x + 2)Why This Is CorrectDivision by an expression can be written as a fraction.The entire expression5x²−3x + 2becomes the denominator.3. QuestionRewrite the expression as a fraction:12r−13Answer Choices•((12r–13)/2)•((12r–13)/1))•(1/(12r–13))Correct Answer(12r–13/1)Why This Is CorrectAny expression can be written as a fraction by placing1 in the denominator.This does not change the value of the expression.

Algebra II - Rational Expressions - Page 6 preview image

Loading page ...

Study Guide4. QuestionRewrite the expression as a fraction:(5b3-2b2+ c7) ÷ (8c + 7b4)Answer ChoicesCorrect AnswerWhy This Is CorrectDivision by a polynomial is written as a fraction.The numerator is the first expression and the denominator is the second.5. QuestionEvaluate the expression:(24x²y²−8xy + 4) ÷ (8b · 0)Answer Choices

Algebra II - Rational Expressions - Page 7 preview image

Loading page ...

Study GuideCorrect AnswerinsolubleWhy This Is CorrectThe denominator contains8b · 0.This means the expression becomesdivision by zero, which isundefined in mathematics.Since division by zero is not allowed, the expression hasno valid solutionand is consideredinsoluble (undefined).3.Simplifying RaƟonal ExpressionsSimplifying arational expressionworks very much like simplifying a regular fraction. The goal is tofactor the numerator and denominator and cancel any common factors.Steps to Simplify a Rational ExpressionTo simplify a rational expression:1.Completely factor the numerator and denominator.2.Cancel any common factorsthat appear in both the numerator and denominator.Onlyfactorscan be canceled—not individual terms.Example 1:Simplify:Step 1: Factor both expressions

Algebra II - Rational Expressions - Page 8 preview image

Loading page ...

Study GuideSo the expression becomes:Step 2: Cancel the common factorThis leaves:Example 2:Simplify:Step 1: Factor each expressionDifference of squares:Sum of cubes:So we get:Step 2: Cancel the common factorResult:

Algebra II - Rational Expressions - Page 9 preview image

Loading page ...

Study GuideExample 3:Simplify:Step 1: Factor the numeratorDifference of squares:Step 2: Rewrite the denominatorStep 3: Cancel the common factorSo we get:Final result:Example 4:Simplify:Step 1: Factor the numerator

Algebra II - Rational Expressions - Page 10 preview image

Loading page ...

Study GuideStep 2: Factor the denominatorRewrite the denominator:Now factor:So the denominator becomes:Step 3: Cancel common factorsCancel:The expression becomes:This can also be written as:orAll forms represent the same simplified expression.

Preview Mode

This document has 107 pages. Sign in to access the full document!

Report

Algebra II - Rational Expressions

Study Now!

Document Details

Related Documents

Algebra II – Word Problems

Algebra II – Sequences and Series

Algebra II - Segments Lines and Inequalities

Algebra II - Relations and Functions

Algebra II – Radicals and Complex Numbers

Algebra II - Quadratics in One Variable

Algebra II – Quadratic Systems

Algebra II – Polynomial Function

Algebra II - Polynomial Arithmetic

Algebra II - Linear Sentences in Two Variables

Company

Explore

Study Tools