Chapter 8 Rational Expressions

Sect. 8.1 Simplifying Rational Expressions

Find the Value(s) of the Variable that Make a Rational Expression Equal Zero and that Make a Rational Expression Undefined Ex. 2 For the rational expression, for what value(s) of the variable (i)does the expression equal zero? (ii) is the expression undefined?

Write a Rational Expression in Lowest Terms

Examples of Writing a Rational Expression in Lowest Terms

Simplify a Rational Expression of the Form

Write Equivalent Forms of a Rational Expression

Define a Rational Function and Find the Domain Ex. 6 Determine the domain of f(x) below.

Sect. 8.2 Multiplying and Dividing Rational Expressions

Multiply Rational Expressions

Divide Rational Expressions

Divide Rational Expressions cont.

Division Problems with Rational Expressions

Find the Least Common Denominator for a Group of Rational Expressions Ex. 1 Find the LCD of each pair:

More Examples of Finding the LCD

Finding the LCD when the denominators are opposites Ex. 3

For a Group of Fractions, Rewrite Each as an Equivalent Fraction with the LCD as its Denominator Ex. 4

Ex. 5 For a Group of Rational Expressions, Rewrite Each as an Equivalent Expression With the LCD as Its Denominator

For a Group of Rational Expressions, Rewrite Each as an Equivalent Expression With the LCD as Its Denominator cont.

Sect. 8.4 Adding and Subtracting Rational Expressions

Another Example of Adding and Subtracting with a Common Denominator

Add or Subtract Rational Expressions with Different Denominators

Add or Subtract Rational Expressions with Different Denominators continued

Another Example of Subtracting Rational Expressions with Different Denominators

Add and Subtract Rational Expressions with Denominators Containing Factors of the Form a - b and b - a Ex. 5

Add and Subtract Rational Expressions with Denominators Containing Factors of the Form a - b and b - a continued

Ex. 1 Mid-Chapter Summary Ex. 2 A = 9 or a = -9

More Review Examples Ex. 3

More Review Examples Ex. 4

Sect. 8.5 Simplifying Complex Fractions

Ex. 2 Simplify a Complex Fraction that has More Than One Term in the Numerator and/or Denominator by Rewriting It as a Division Problem

Simplify a Complex Fraction that has More Than One Term in the Numerator and/or Denominator by Rewriting It as a Division Problem

Ex. 3 Simplify a Complex Fraction That Has More than One Term in the Numerator and/or Denominator by Multiplying by the LCD

Sect. 8.6 Solving Rational Equations Ex. 1 Rational Expression vs. Rational Equation

Rational Expression vs. Rational Equation continued

Solve Rational Equations Ex. 2

Another Example of Solving Rational Equations

Another Example of Solving Rational Equations

Example 4 continued

Solve a Proportion Ex. 5 The answer checks.

Solve an Equation for a Specific Variable Ex. 6

Another Example of Solving an Equation for a Specific Variable

Sect. 8.7 Applications of Equations Containing Rational Expressions Problems Involving Proportion Sect. 8.7 Applications of Equations Containing Rational Expressions X+ 126 = 168

Problems Involving Distance, Rate and Time

Rate, Time, Distance Problem continued

Rate, Time, Distance Problem continued

Solve Problems Involving Work

Work Problem continued