University:
California State University, Northridge
Course:
MATH 320 | Foundations of Higher Mathematics
Academic year:

2024
Views:

310

Pages:

10
Author:

Ty Gilbert

§ 14.2 Multiplying and Dividing Rational Expressions Multiplying Rational Expressions Multiplying rational expressions when P, Q, R, and S are polynomials with Q ≠ 0 and S ≠ 0. P R PR ⋅ = Q S QS 15 Multiplying Rational Expressions Note that after multiplying such expressions, our result may not be in simplified form, so we use the following techniques. Multiplying rational expressions 1) Factor the numerators and denominators. 2) Multiply the numerators and multiply the denominators. 3) Simplify or write the product in lowest terms by applying the fundamental principle to all common factors. 16 Multiplying Rational Expressions Example Multiply the following rational expressions. 2 ⋅3⋅ x ⋅ x ⋅5⋅ x 6 x 5x 1 = ⋅ = 3 10 x 12 2 ⋅ 5 ⋅ x ⋅ x ⋅ x ⋅ 2 ⋅ 2 ⋅ 3 4 2 17 Multiplying Rational Expressions Example Multiply the following rational expressions. 2 ( m − n) m (m − n)(m − n) ⋅ m ⋅ 2 = = m + n m − mn (m + n) ⋅ m(m − n) m−n m+n 18 Dividing Rational Expressions Dividing rational expressions when P, Q, R, and S are polynomials with Q ≠ 0, S ≠ 0 and R ≠ 0. P R P S PS ÷ = ⋅ = Q S Q R QR 19 Dividing Rational Expressions When dividing rational expressions, first change the division into a multiplication problem, where you use the reciprocal of the divisor as the second factor. Then treat it as a multiplication problem (factor, multiply, simplify). 20 Dividing Rational Expressions Example Divide the following rational expression. 2 2 25 ( x + 3) 5 x + 15 ( x + 3) ⋅ = ÷ = 5 5 x + 15 5 25 ( x + 3)( x + 3) ⋅ 5 ⋅ 5 = x+3 5 ⋅ 5( x + 3) 21 Units of Measure Converting Between Units of Measure Use unit fractions (equivalent to 1), but with different measurements in the numerator and denominator. Multiply the unit fractions like rational expressions, canceling common units in the numerators and denominators. 22 Units of Measure Example Convert 1008 square inches into square feet.  1 ft   1 ft  (1008 sq in) ⋅  = ⋅  12 in   12 in   1 ft   1 ft  (2·2·2·2·3·3·7 in · ⋅  = ⋅ ⋅ ⋅ 2 ⋅ 2 ⋅ 3 in 2 2 3 in     in) 7 sq. ft. 23