G. Math Can be Rational

Pre-Calculus 20 P20.3

Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: equivalent forms of expressions operations on expressions solving equations that can be simplified to linear or quadratic equations.

Key Terms

Factoring Review

1. Rational Expressions

    P20.3

Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: equivalent forms of expressions operations on expressions

 Investigate p. 311 #2-8

 Non-Permissible Values  When you are using Rational expressions (RE), you have to identify any values to be excluded and are called Non Permissible Values  Non-Permissible Value make the denominator equal zero

Example 1

 Equivalent Rational Expressions  If you multiply or divide a rational expression by 1 you do not change the value

 Simplifying Rational Expressions  To simplify a rational expression, divide both the numerator and denominator by any factors that are common to both  For example

 When a rational expression is in simplest form there are no common factors in the numerator and denominator.

Example

Example 3

Key Ideas p. 317

Practice

 Ex. 6.1 (p.317) #1-8 odds in each, 9-15, 17 #8, 9-25 odds

2. Multiplying and Dividing Rational Expressions     P20.3

Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: equivalent forms of expressions operations on expressions

 Investigate p. 219

 When multiplying rational expressions, you follow procedures similar to those for multiplying rational numbers

 When dividing rational expressions follow similar procedures to dividing rational numbers

Example 1

Example 2

Example 3

Key Ideas p. 221

Practice

 Ex. 6.2 (p.327) #1-16 #1-21odds

3. Adding and Subtracting Rational Expressions     P20.3

Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: equivalent forms of expressions operations on expressions

 Investigate p. 331

 To add or subtract rational expressions we follow the same rules as rational numbers.

 Same Denominator – simply add or subtract the numerators and leave the denominators the same  Different Denominator – first get a common denominator then simply add or subtract the tops

 For example,

 Lowest Common Denominator is best to use because then your final answer is already in simplest form.

Example 1

Example 2

Key Ideas p. 335

Practice

 Ex. 6.3 (p.336) #1-10 odds in each, 11-19 odds #6-10 odds in each, 11-23 odds

4. Equations Containing Rationals

     P20.3

Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: equivalent forms of expressions operations on expressions solving equations that can be simplified to linear or quadratic equations.

4. Equations Containing Rationals

 Investigate p. 341

 Rational Equations can be used to solve several different types of Real World Problems which we will see.

 Working with a rational equation is similar to working with a rational expression except for on big difference. What you do to one side of the = sign you have to do to the other side

 Steps to Solve: 1.

2.

3.

4.

5.

If you can factor.

Identify any non-permissible values Multiply both sides of the equation by the LCD Solve by isolating variable on one side of = sign Check your answers

 For example

 Non-permissible values must be indentified in the original equation and cannot be used as a final answer.

Example 1

Example 2

Example 3

Example 4

Key Ideas p. 348

Practice

 Ex. 6.4 (p. 348) #1-14 #1-21 odds