1. Chapter 8 – Rational Expressions and Equations
8.1 – Multiplying and Dividing Rational Expressions

2. 8.1 – Multiplying and Dividing Rational Expressions
Today we will be learning how to:
Simplify rational expressions
Simplify complex fractions

3. 8.1 – Multiplying and Dividing Rational Expressions
Rational expression – a ratio of two polynomial expressions
8 + x
13 + x
Because variables in algebra often represent real numbers, operations with rational numbers and rational expression are similar.

4. 8.1 – Multiplying and Dividing Rational Expressions
To write a fraction in simplest form, you divide both the numerator and denominator by their greatest common factor (GCF).
To simplify a rational expression, you use similar techniques

5. 8.1 – Multiplying and Dividing Rational Expressions
Example 1
Simplify 3y(y + 7)/(y + 7)(y2 – 9)
Under what conditions is this expression undefined?

6. 8.1 – Multiplying and Dividing Rational Expressions
Example 2
For what values of p is p2 + 2p – 3/p2 – 2p – 15 undefined?

7. 8.1 – Multiplying and Dividing Rational Expressions
Example 3
Simplify a4b – 2a4/2a3 – a3b

8. 8.1 – Multiplying and Dividing Rational Expressions
Remember:
To multiply two fractions, you multiply the numerators and multiply the denominators
5/6 · 4/15
To divide two fractions, you multiply by the multiplicative inverse (reciprocal), of the divisor
3/7 ÷ 9/14

9. 8.1 – Multiplying and Dividing Rational Expressions
Multiplying Rational Expressions
To multiply two rational expressions, multiply the numerators and the denominators
For all rational expressions a/b and c/d, a/b · c/d = ac/bd if b ≠ 0 and d ≠ 0
Dividing Rational Expressions
To divide two rational expressions, multiply by the reciprocal of the divisor
For all rational expressions a/b and c/d, a/b ÷ c/d = a/b · d/c = ad/bc if b ≠ 0, c ≠ 0, and d ≠ 0

10. 8.1 – Multiplying and Dividing Rational Expressions
Example 4
Simplify each expression
8x/21y3 · 7y2/16x3
10ps2/3c2d ÷ 5ps/6c2d2

11. 8.1 – Multiplying and Dividing Rational Expressions
Example 5
Simplify each expression
(k – 3)/(k + 1) · (1 – k2)/(k2 – 4k + 3)
(2d + 6)/(d2 + d – 2) ÷ (d + 3)/(d2 + 3d + 2)

12. 8.1 – Multiplying and Dividing Rational Expressions
Complex fraction – rational expression whose numerator and/or denominator contains a rational expression
(a/5)/3b
(3/t)/t+5
[(m2 – 9)/8]/[(3 – m)/12]
To simplify a complex fraction, rewrite it was a division expression and use the rules for division

13. 8.1 – Multiplying and Dividing Rational Expressions
Example 6
Simplify x2
9x2 – 4y2 x3
2y – 3x

14. 8.1 – Multiplying and Dividing Rational Expressions
HOMEWORK Page 446 #17 – 35 odd, 36 – 37