1. Chapter 12 Final Exam Review

2. Section 12.4 “Simplify Rational Expressions” A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction) of two polynomials where the denominator is not 0. A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction) of two polynomials where the denominator is not 0.

3. Simplify Rational Expressions To simplify a rational expression, you can factor the numerator and denominator and then divide out any common factors. To simplify a rational expression, you can factor the numerator and denominator and then divide out any common factors. A rational expression is in SIMPLEST FORM if the numerator and denominator have no factors in common other than 1. A rational expression is in SIMPLEST FORM if the numerator and denominator have no factors in common other than 1.

4. Simplify the rational expression, if possible. Factor Factor Recognizeopposites Multiply by -1 Rewrite (z-5) as -(z+5)

5. Section 12.5 “Multiply and Divide Rational Expressions” Multiplying and dividing rational expressions is similar to multiplying and dividing fractions. Be sure to simplify your answer. Look to cancel like terms when multiplying or dividing. Multiply by reciprocal, then look to cancel terms.

6. Multiply by reciprocal Find the product or quotient. EXAMPLE 1

7. Find the product. EXAMPLE 2 Multiply numerator and denominator. Factor and look for common factors to cancel.

8. Find the quotient. Try it out. EXAMPLE 2 Multiply numerator and denominator. Factor and look for common factors to cancel. Multiply by reciprocal

9. Find the product. EXAMPLE 3 Multiply numerator and denominator. Factor and look for common factors to cancel.

10. Section 12.6 “Add and Subtract Rational Expressions” Adding and subtracting rational expressions is similar to adding and subtracting fractions. Be sure to simplify your answer. Denominator must be COMMON!!!

11. Find the sum or difference. EXAMPLE 5 LCD = (x+5)(x – 2)(x + 4)

12. Section 12.7 “Solve Rational Equations” A RATIONAL EQUATION is an equation that contains one or more rational expressions. One method for solving a rational equation is to use the cross products property. (You can use this method when both sides of the equation are single rational expressions).

13. Cross multiply Solve the equation. Check your solution. Check for extraneous solutions y = 5 y = -3