Rational Functions and Variations Simplifying Rational Expression

Rational Function (7.1)  

Inverse Variation(7.1)  

Modeling(7.1) A group of students in the chess club want to rent a bus to take them to a national chess competition. The bus cost $1500 to rent and can hold up to 60 people. Write an equation that models the given information. Cost per student if 30 students take the bus. What is a reasonable domain and range?

Inverse Variation(7.1)  

Direct Variation(7.1)  

Car Repair(7.1) The cost for labor at an auto repair shop is directly proportional to the time the mechanic spends working on the car. If the mechanic works on the car for five hours the labor cost is $325. Write an equation that models the labor cost at the auto shop. What is the labor cost for two hours of work?

Domain(7.1)  

Example (7.1)  

Simplify all fractions #1 Rule (7.2) Simplify all fractions

Methods (7.2) Factor Long Division Synthetic Division

Factor (7.2)  

Special case factoring 7(x – 5) (5 – x) Rewrite the denominator with the variable expression first 7(x – 5) 7(x – 5) 7(x – 5) (5 – x) (-x + 5) -1(x – 5) -7

Long Division  

Performing Synthetic Division Condenses the steps of long division without all the detail. Performing Synthetic Division The divisor (polynomial in the denominator) must be a binomial of the form x – c Use only the coefficients of each term and not the variables

Example  

Practice  

Multiplying/Dividing(7.3) The rules for fractions still apply when working with rational expressions! Multiplication 2ox • 6xy 18y2 10 Factor the numerator and the denominator Divide out common factor Rewrite as a single fraction in factored form

Dividing x + 3 • x – 7 = x + 3 x – 7 x – 4 x – 4 Keep Change Flip Factor the numerator and denominator (if possible) Divide out common factors and leave in factored form x + 3 • x – 7 = x + 3 x – 7 x – 4 x – 4

Adding/Subtracting  

Practice  

Practice h + 14 + h – 6 (h + 5) (h – 4) h – 4 a + 2 + a – 3 a2 + 5a – 6 a2 + 8a + 12

Subtraction Be careful! The numerator of the second fraction changes sign in subtraction. x2 + 5x - 3x + 8 (x + 3)(x + 4) (x + 3)(x + 4)

Complex Fraction