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

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

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.

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

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

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

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

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

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

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

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)

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

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

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