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Unformatted text preview: d numerator. Dividing by these common xy factors, we are left with ⋅ . Finally, we multiply the resulting fractions, giving an answer of xy.
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x3 y3 . 2 and y x2 Example: Divide Solution: 15a 2 b by 5a3. 2 We invert the divisor and multiply.
15a 2 b 1 ⋅3 2 5a We can divide the first numerator and second denominator by 5a2, giving 3b 1 3b ⋅ or . 2a 2a www.petersons.com 162 Chapter 11 Exercise 3
Work out each problem. Circle the letter that appears before your answer. 1.
x2 y4 Find the product of 3 and 5 y x y2 4. Divide 4abc by (A) (B) (C) (D) (E)
8a 3 b 2 c 3d 2 a 2a 2 b 3d 2 (A) (B) (C) (D) (E) 2. x y 3 x3 x3 y x8 y7 x y
b c 6cd 2 2ac bd 2 6cd 2 a 5cd 2 a
3a 2 c 4 by 6ac2 4b2 Multiply c by (A) (B) (C) (D) (E)
b c2 c2 b 5. Divide (A) (B) (C) (D) (E) b c bc2 3. ax x Divide by by y ax 2 (A) (B) (C) (D) (E) by 2 b a a b by 2
ax 2 ay bx ac 2 8b 2 ac 2 4b2 4b2 ac 2 8b 2 ac 2 ac 2 6b 2 www.petersons.com Factoring and Algebraic Fractions 163 4. COMPLEX ALGEBRAIC FRACTIONS
Complex algebraic fractions are simplified by the same methods reviewed earlier for arithmetic fractions. To eliminate the fractions within the fraction, multiply each term of the entire complex fraction by the lowest quantity that will eliminate them all. Example:
3 Simplify x Solution: + 6 2 y We must multiply each term by xy, giving 3y + 2 x . 6 xy No more simplification is possible beyond this. Remember never to cancel terms or parts of terms. We may only simplify by dividing factors. Exercise 4
Work out each problem. Circle the letter that appears before your answer. 1.
13 − 52 Simplify 3 4 15 (A) 26 15 (B) − 26 3. (C) (D) (E) 2
26 15 26 − 15 11 − xy Simplify 1 1 + xy x−y (A) x + y x+y (B) x − y y− x (C) x+y (D) (E) 4. –1 –xy 2. a x2 Simplify a 2 x x (A) a 1 1 Simplify 1 + x 1 y x+y (A) x (B) (C) (D) (E) 5. 2y x+1
y +1 x x +1 y (B) (C) a2 x 1 ax (D) (E) ax
a x 1 Simplify 2 + t 2 t2 (A) (B) (C) (D) (E) t2 + t t3 2t + 1 2 t+1
4+t 2 www.petersons.com 164 Chapter 11 5. USING FACTORING TO FIND MISSING VALUES
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at EmbryRiddle FL/AZ.
 Spring '10
 Colon
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