Transcript Document
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.
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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