Module :MA0001NP Foundation Mathematics Lecture Week 6.

Slides:

Advertisements

Similar presentations

Adding and Subtracting Rational Expressions:

Advertisements

Multiplying and Dividing Rational Expressions

Algebraic Fractions and Rational Equations. In this discussion, we will look at examples of simplifying Algebraic Fractions using the 4 rules of fractions.

STROUD Worked examples and exercises are in the text PROGRAMME F7 PARTIAL FRACTIONS.

EXAMPLE 2 Rationalize denominators of fractions Simplify

Sec. 9-4: Rational Expressions. 1.Rational Expressions: Expressions (NOT equations that involve FRACTIONS). We will be reducing these expressions NOT.

Objectives Add and subtract rational expressions.

RATIONAL EXPRESSIONS. EVALUATING RATIONAL EXPRESSIONS Evaluate the rational expression (if possible) for the given values of x: X = 0 X = 1 X = -3 X =

CHAPTER 6 Rational Expressions and Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 6.1Multiplying and Simplifying Rational Expressions.

Copyright © Cengage Learning. All rights reserved. Rational Expressions and Equations; Ratio and Proportion 6.

RATIONAL EXPRESSIONS. Definition of a Rational Expression A rational number is defined as the ratio of two integers, where q ≠ 0 Examples of rational.

Simplify a rational expression

Section 8.2: Multiplying and Dividing Rational Expressions.

Solving Rational Equations On to Section 2.8a. Solving Rational Equations Rational Equation – an equation involving rational expressions or fractions…can.

Warm Up Add or subtract –

Operations on Rational Expressions. Rational expressions are fractions in which the numerator and denominator are polynomials and the denominator does.

Chapter 12 Final Exam Review. Section 12.4 “Simplify Rational Expressions” A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction)

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

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

STARTER Factorise the following: x2 + 12x + 32 x2 – 6x – 16

8.5 – Add and Subtract Rational Expressions. When you add or subtract fractions, you must have a common denominator. When you subtract, make sure to distribute.

5-3 Adding and subtracting rational functions

Module: 0 Part 4: Rational Expressions

Multiplying and Dividing Rational Expressions

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

Objectives Add and subtract rational expressions.

Adding and Subtracting Rational Expressions

8.4 Multiply and Divide Rational Expressions

Solving Two-Step and 3.1 Multi-Step Equations Warm Up

(x+2)(x-2).  Objective: Be able to solve equations involving rational expressions.  Strategy: Multiply by the common denominator.  NOTE: BE SURE TO.

Holt McDougal Algebra Multiplying and Dividing Rational Expressions Simplify rational expressions. Multiply and divide rational expressions. Objectives.

Partial Fractions A rational function is one expressed in fractional form whose numerator and denominator are polynomials. A rational function is termed.

STROUD Worked examples and exercises are in the text Programme F8: Partial fractions PROGRAMME F8 PARTIAL FRACTIONS.

Welcome to Algebra 2 Rational Equations: What do fractions have to do with it?

Operations on Rational Expressions MULTIPLY/DIVIDE/SIMPLIFY.

A rational expression is a fraction with polynomials for the numerator and denominator. are rational expressions. For example, If x is replaced by a number.

Chapter 6 Rational Expressions and Equations

PROGRAMME F7 PARTIAL FRACTIONS.

Objectives Add and subtract rational expressions.

Operations on Rational algebraic expression

Section R.6 Rational Expressions.

8.4 Adding and Subtracting Rational Expressions

Warm Up Add or subtract –

Warm Up Add or subtract –

Warm Up Add or subtract –

Do Now: Multiply the expression. Simplify the result.

EXAMPLE 2 Rationalize denominators of fractions Simplify

MTH1170 Integration by Partial Fractions

Simplify each expression. Assume all variables are nonzero.

Multiplying and Dividing Rational Expressions

1 Introduction to Algebra: Integers.

Warm Up Add or subtract –

Multiplying and Dividing Rational Expressions

Without a calculator, simplify the expressions:

Look for common factors.

Review Algebra.

LESSON 6–4 Partial Fractions.

Chapter R Algebra Reference.

Adding/Subtracting Like Denominator Rational Expressions

Rational Expressions and Equations

Warmup Find the exact value. 1. √27 2. –√

Multiplying and Dividing Rational Expressions

Rational Expressions and Equations

PROGRAMME F7 PARTIAL FRACTIONS.

A rational expression is a quotient of two polynomials

Multiplying and Dividing Rational Expressions

College Algebra Chapter 5 Systems of Equations and Inequalities

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Presentation transcript:

Module :MA0001NP Foundation Mathematics Lecture Week 6

Rational Expressions P, Q, R, and S are polynomials Addition Operation Multiplication Subtraction Division Notice the common denominator Reciprocal and Multiply

Addition Simplify

Addition Simplify

Subtraction Simplify

Subtraction Simplify 4

Multiplication Simplify

Multiplication Simplify Factorising (2x-6) 3

Division Simplify 2 2

Solve

Partial fractions Programme F7: Partial fractions Consider the following combination of algebraic fractions: The fractions on the left are called the partial fractions of the fraction on the right.

Partial fractions Find the partial fractions of the following Programme F7: Partial fractions

Partial fractions It is assumed that a partial fraction break down is possible in the form: The assumption is validated by finding the values of A and B. Partial fractions

To find the values of A and B the two partial fractions are added to give:

Partial fractions Programme F7: Partial fractions Since: And since the denominators are identical the numerators must be identical as well. That is:

Partial fractions Programme F7: Partial fractions Consider the identity: Therefore: Therefore Therefore:

Denominators with quadratic factors A similar procedure is applied if one of the factors in the denominator is a quadratic. For example: This results in:

Denominators with quadratic factors Equating coefficients of powers of x yields: Three equations in three unknowns with solution:

Denominators with repeated factors Repeated factors in the denominator of the original fraction of the form: give partial fractions of the form: Partial fractions

Denominators with repeated factors Partial fractions Similarly, repeated factors in the denominator of the original fraction of the form: give partial fractions of the form:

Partial fractions Programme F7: Partial fractions Find the partial fractions for the following expressions : 1.7x+18/(x+2)(x+3) 2.2x-7/x²+5x /2x²+15x x-11/x²-5x+4 5.3x+11/2x²+3x-2

Partial fractions Programme F7: Partial fractions Find the partial fractions for the following expressions : 6.x+21/2(2x+3)(3x-2) 7. x-35/x²-25 8.x-4/x²-6x+9 9.5x+4/-x²-x x-5/9x²-6x+1