1. 7.1/7.2 – Rational Expressions: Simplifying, Multiplying, and Dividing
Math 51
7.1/7.2 – Rational Expressions: Simplifying, Multiplying, and Dividing

2. A rational expression is a _________________ divided by a _________________. ex: 50𝑥 10−𝑥 3𝑥+1 𝑥 2 −3𝑥+2 𝑥 2 +3𝑥𝑦−10 𝑦 2 3 𝑥 2 −7𝑥𝑦+2 𝑦 2

3. A rational expression is a _________________ divided by a _________________. ex: 50𝑥 10−𝑥 3𝑥+1 𝑥 2 −3𝑥+2 𝑥 2 +3𝑥𝑦−10 𝑦 2 3 𝑥 2 −7𝑥𝑦+2 𝑦 2
polynomial

4. A rational expression is a _________________ divided by a _________________. ex: 50𝑥 10−𝑥 3𝑥+1 𝑥 2 −3𝑥+2 𝑥 2 +3𝑥𝑦−10 𝑦 2 3 𝑥 2 −7𝑥𝑦+2 𝑦 2
polynomial
polynomial

5. A rational expression is a _________________ divided by a _________________. ex: 50𝑥 10−𝑥 3𝑥+1 𝑥 2 −3𝑥+2 𝑥 2 +3𝑥𝑦−10 𝑦 2 3 𝑥 2 −7𝑥𝑦+2 𝑦 2
polynomial
polynomial

6. Note: Rational expressions are undefined when the denominator is equal to 0. Ex 1. Find any values of the variable for which each rational expression is undefined. 𝑥+5 3𝑥+2 9 𝑥 2 𝑥 2 −5𝑥+6 2𝑥 𝑥 2 +1

7. Note: Rational expressions are undefined when the denominator is equal to 0. Ex 1. Find any values of the variable for which each rational expression is undefined. 𝑥+5 3𝑥+2 9 𝑥 2 𝑥 2 −5𝑥+6 2𝑥 𝑥 2 +1

8. Note: Rational expressions are undefined when the denominator is equal to 0. Ex 1. Find any values of the variable for which each rational expression is undefined. 𝑥+5 3𝑥+2 9 𝑥 2 𝑥 2 −5𝑥+6 2𝑥 𝑥 2 +1

9. Note: Rational expressions are undefined when the denominator is equal to 0. Ex 1. Find any values of the variable for which each rational expression is undefined. 𝑥+5 3𝑥+2 9 𝑥 2 𝑥 2 −5𝑥+6 2𝑥 𝑥 2 +1

10. Simplifying Rational Expressions
Note: Just like any fraction, a rational expression is in lowest terms if the GCF of the numerator and denominator is 1 (that is, if there aren’t any common factors on top and bottom). Ex 2. Write the following rational expression in lowest terms. 3𝑥−12 5𝑥−20

11. Simplifying Rational Expressions
Note: Just like any fraction, a rational expression is in lowest terms if the GCF of the numerator and denominator is 1 (that is, if there aren’t any common factors on top and bottom). Ex 2. Write the following rational expression in lowest terms. 3𝑥−12 5𝑥−20

12. Simplifying Rational Expressions
Ex 3. Write the following rational expression in lowest terms. 𝑥 2 +2𝑥−8 2 𝑥 2 −𝑥−6

13. Simplifying Rational Expressions
Ex 4. Write the following rational expression in lowest terms. 𝑥−𝑦 𝑦−𝑥

14. Simplifying Rational Expressions
Ex 5. Write the following rational expression in lowest terms. 4 𝑥 2 −9 6−4𝑥

15. Multiplying and Dividing Rational Expressions
Rational expressions work just like regular fractions when it comes to multiplication and division. Ex 6. Multiply. Write your answer in lowest terms. 𝑥+𝑦 2𝑥 ⋅ 𝑥 2 𝑥+𝑦 2

16. Multiplying and Dividing Rational Expressions
Rational expressions work just like regular fractions when it comes to multiplication and division. Ex 6. Multiply. Write your answer in lowest terms. 𝑥+𝑦 2𝑥 ⋅ 𝑥 2 𝑥+𝑦 2

17. Ex 7. Multiply. Write your answer in lowest terms

18. Ex 8. Divide. Write your answer in lowest terms