Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic...

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Transcript of Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic...

$Page 1: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Algebra

11-3 and 11-4

$Page 2: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Simplifying Rational Expressions

• A rational expression is an algebraic fraction whose numerator and denominator are polynomials (Can’t have ZERO in the denominator)

$Page 3: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Example 1

$Page 4: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Factor to Simplify

• Example 2

$Page 5: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

TRICKY– Recognize opposites

• Example 5

$Page 6: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Rational Functions – find the zeros

• Example 6

$Page 7: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Multiplying and Dividing Rational Expressions

• Same as any fraction, multiply numerators and multiply denominators

• When dividing, multiply by the RECIPROCAL!!!

$Page 8: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Example 1

$Page 9: Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.$

Example 3

Turn Arround and Numerator and Denominator IN BUSINESS STRATEGY II

11.4 Multiply and Divide Rational Expressions. SIMPLIFYING RATIONAL EXPRESSIONS Step 1: Factor numerator and denominator “when in doubt, write it out!!”

Class Example - Rationals Rational numbers are represented by the ratio of two integers, a numerator and a denominator, e.g., 2/3. This is opposed to irrational.

$Algebra 3-4 Unit 4 Rational 4... · Rational expression: a fraction that has polynomials in the numerator and/or denominator. To multiply two rational expressions: factor, cancel$

Algebra 3-4 Unit 4 Rational 4... · Rational expression: a fraction that has polynomials in the numerator and/or denominator. To multiply two rational expressions: factor, cancel

$Solving Rational Equations. 2 Rational Expression A rational expression is a fraction with polynomials for the numerator and denominator. are rational.$

Solving Rational Equations. 2 Rational Expression A rational expression is a fraction with polynomials for the numerator and denominator. are rational.

Rational and Radical Functions...Graphing Rational Functions 1.Evaluate the function at 0 to find the5-intercept 2.Factor the numerator and denominator 3.For factors in the numerator

$Partial Fractions - Austin Community College - Start …Thomason - Spring 2012) Partial Fractions A rational function is a fraction in which both the numerator and denominator are$

Partial Fractions - Austin Community College - Start …Thomason - Spring 2012) Partial Fractions A rational function is a fraction in which both the numerator and denominator are

$Rational and Irrational Numbers A rational number is a number that can be expressed as a fraction or ratio (rational). The numerator and the denominator.$

Rational and Irrational Numbers A rational number is a number that can be expressed as a fraction or ratio (rational). The numerator and the denominator.

9-3 Rational Functions (& their graphs) · 09-03-2014 · 9-3 Rational Functions (& their graphs) A rational function is one that has polynomials in the numerator and the denominator.

$Add and Subtract Rational Expressions€¦ · Simplifying Complex Fractions A complex fraction is a fraction that contains a fraction in its numerator or denominator. A complex fraction$

Add and Subtract Rational Expressions€¦ · Simplifying Complex Fractions A complex fraction is a fraction that contains a fraction in its numerator or denominator. A complex fraction

$6 Solving Rational Equations - Amazon S3 · 6 Solving Rational Equations When simplifying complex fractions in the previous section, we saw that multiplying both numerator and denominator$

6 Solving Rational Equations - Amazon S3 · 6 Solving Rational Equations When simplifying complex fractions in the previous section, we saw that multiplying both numerator and denominator

Operations with Fractions. Parts of a Fractions Numerator Denominator.

$HOW TO IDENTIFY FRACTIONS Introducing: whole number numerator fraction bar denominator improper.$

HOW TO IDENTIFY FRACTIONS Introducing: whole number numerator fraction bar denominator improper.

$MTH 05 Lecture Notes - City University of New York...Chapter 1 Review of fractions Vocabulary • Whole numbers • Integers • Fraction • Numerator • Denominator • Rational$

MTH 05 Lecture Notes - City University of New York...Chapter 1 Review of fractions Vocabulary • Whole numbers • Integers • Fraction • Numerator • Denominator • Rational

$Fractions Shelby Ferreira. Vocabulary Numerator Denominator Proper fraction Improper fraction Mixed number.$

Fractions Shelby Ferreira. Vocabulary Numerator Denominator Proper fraction Improper fraction Mixed number.

Polynomial and Rational Expressions...Given Two Rational Expressions, Add or Subtract them 1.Factor the numerator and denominator 2.Find the LCD of the expressions 3.Multiply the expressions

$Fractions FractionsFractionsncert.nic.in/textbook/pdf/femh107.pdf · , the numerator is bigger than the denominator . The fractions, where the numerator is bigger than the denominator$

Fractions FractionsFractionsncert.nic.in/textbook/pdf/femh107.pdf · , the numerator is bigger than the denominator . The fractions, where the numerator is bigger than the denominator

Chapter 240p6zu91z1c3x7lz71846qd1-wpengine.netdna-ssl.com › wp-content … · 48 Chapter 2 Section 2.1 Practice 1. 9 numerator 2 denominator ← ← 2. 10 numerator 17 denominator

$Topic 4 Real Numbers. 8.1.1 Rational Numbers To express a fraction as a decimal, divide the numerator by the denominator.$

Topic 4 Real Numbers. 8.1.1 Rational Numbers To express a fraction as a decimal, divide the numerator by the denominator.

Maine IHOC Pediatric Measures Master List with Numerator ... · Numerator/Denominator Measure Steward Measure Type 1e. Three hepatitis B (HepB) Numerator: Of those in the denominator,

Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic...

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Transcript of Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic...