Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P...

17
Rational Expressions

Transcript of Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P...

Page 1: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Rational Expressions

Page 2: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Rational ExpressionAn expression that can be

written in the form P/Q, where P and Q are polynomials and Q

is not equal to zero.Examples

Page 3: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Restrictions on Variables

1.The denominator cannot equal zero.

2.The restrictions indicate when the denominator equals zero.

3.Factor the denominator completely and set each factor not equal to zero.

4.Solve for the given variable.

Page 4: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Domain of A FunctionAll the x values in a given

function.

Page 5: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

State the restrictions on the domain and state the domain

of the function.

Page 6: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Simplifying1.Factor each expression

completely

2.List any restrictions

3.Divide out any common factors

4.Simplify and leave in factored form

Page 7: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Simplify the following rational expressions and state the

domain

Page 8: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Multiplying and Dividing1.Change division to

multiplication of the inverse

2.Factor each expression completely

3.Divide out any common factors

4.Simplify and leave in factored form

Page 9: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Perform the indicated operation and leave your answer in factored form.

Page 10: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Adding and Subtracting1.Factor each denominator

completely

2.Find the LCM of the denominators

3.Multiply each term by the LCM

4.Simplify the numerator

5.The denominator is the LCM

6.Simplify and leave in factored form

Page 11: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Perform the indicated operation and leave your answer in factored form.

Page 12: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Perform the indicated operation and leave your answer in factored form.

Page 13: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Complex Rational1.Factor each denominator

completely

2.Find the LCM

3.Multiply numerator / denominator by the LCM

4.Combine all like terms

5.Simplify and leave in factored form

Page 14: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Perform the indicated operation and leave your answer in

factored form.

Page 15: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Perform the indicated operation and leave your answer in

factored form.

Page 16: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Perform the indicated operation and leave your answer in

factored form.

Page 17: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Perform the indicated operation and leave your answer in

factored form.


Precalc hw #3 Rational Expressions - Mrs. Sevilla's Math Classsevillaj.weebly.com/.../8/4/7784014/precalc_hw_3_rational_expressio… · Rational Expressions • A rational expression

Precalc hw #3 Rational Expressions - Mrs. Sevilla's Math Classsevillaj.weebly.com/.../8/4/7784014/precalc_hw_3_rational_expressio… · Rational Expressions • A rational expression

6.1 The Fundamental Property of Rational Expressions Rational Expression – has the form: where P and Q are polynomials with Q not equal to zero. Determining.

6.1 The Fundamental Property of Rational Expressions Rational Expression – has the form: where P and Q are polynomials with Q not equal to zero. Determining.

Rational Expression Simplification with Algebraic Side ...

Rational Expression Simplification with Algebraic Side ...

Rational Algebraic Expression

Rational Algebraic Expression

Simplifying Rational Expression

Simplifying Rational Expression

I Rational Expression Worksheet #2: Simplifying

I Rational Expression Worksheet #2: Simplifying

Rational Expressions A rational expression is any expression that consists of a polynomial divided by a nonzero polynomial. Examples of rational expressions:

Rational Expressions A rational expression is any expression that consists of a polynomial divided by a nonzero polynomial. Examples of rational expressions:

Chapter 12: Rational Expressions and · PDF fileRational Expressions and Equations • inverse variation (p. 642) • rational expression (p. 648) ... • Lesson 12-9 Solve rational

Chapter 12: Rational Expressions and · PDF fileRational Expressions and Equations • inverse variation (p. 642) • rational expression (p. 648) ... • Lesson 12-9 Solve rational

ASSIGNMENTS 1 Rational Numbers and . (Any) Q.3. Find Class 8 Mathematics... · Module – 1 Rational Numbers ... (MCQ)Rational Numbers 1. The additive identity for rational numbers

ASSIGNMENTS 1 Rational Numbers and . (Any) Q.3. Find Class 8 Mathematics... · Module – 1 Rational Numbers ... (MCQ)Rational Numbers 1. The additive identity for rational numbers

Rational Expressions Simplifying. Simplifying Rational Expressions The objective is to be able to simplify a rational expression.

Rational Expressions Simplifying. Simplifying Rational Expressions The objective is to be able to simplify a rational expression.

9.4 Multiply and Divide Rational Expressions VOCABULARY Simplified form of a rational expression.

9.4 Multiply and Divide Rational Expressions VOCABULARY Simplified form of a rational expression.

Simplify each expression. each expression ... Is the sum rational or irrational? Is the product of a nonzero ... Examine the sum of several pairs of rational and irrational numbers:

Simplify each expression. each expression ... Is the sum rational or irrational? Is the product of a nonzero ... Examine the sum of several pairs of rational and irrational numbers:

Ch.9.1-9.4 Rational Expressions and Equations · Chapter 9 Rational Expressions and Equations 9.1 — 9.6 Key Concepts 9.1 Simplifying Rational Expressions Q) What is a rational expression?

Ch.9.1-9.4 Rational Expressions and Equations · Chapter 9 Rational Expressions and Equations 9.1 — 9.6 Key Concepts 9.1 Simplifying Rational Expressions Q) What is a rational expression?

Jeopardy Inverses Geometric Sequences Exponential Functions Rational Exponents Random Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q.

Jeopardy Inverses Geometric Sequences Exponential Functions Rational Exponents Random Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q.

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.

Jeopardy Adding Subtracting X & /Rational # Other Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy.

Jeopardy Adding Subtracting X & /Rational # Other Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy.

R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

Section 6.1 Rational Expressions. OBJECTIVES Determine the values that make a rational expression undefined. A.

Section 6.1 Rational Expressions. OBJECTIVES Determine the values that make a rational expression undefined. A.

The Fundamental Property of Rational Expressions Find the numerical value of a rational expression. Find the values of the variable for which a rational.

The Fundamental Property of Rational Expressions Find the numerical value of a rational expression. Find the values of the variable for which a rational.

Rational Expressions Simplifying. Polynomial – The sum or difference of monomials. Rational expression – A fraction whose numerator and denominator are.

Rational Expressions Simplifying. Polynomial – The sum or difference of monomials. Rational expression – A fraction whose numerator and denominator are.