7.4E: Exercises
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Simplify a Complex Rational Expression by Writing it as Division
In the following exercises, simplify each complex rational expression by writing it as division.
1. 2aa+44a2a2−16
- Answer
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a−42a
2. 3bb−5b2b2−25
3. 5c2+5c−1410c+7
- Answer
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12(c−2)
4. 8d2+9d+1812d+6
5. 12+5623+79
- Answer
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1213
6. 12+3435+710
7. 23−1934+56
- Answer
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2057
8. 12−1623+34
9. nm+1n1n−nm
- Answer
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n2+mm−n2
10. 1p+pqqp−1q
11. 1r+1t1r2−1t2
- Answer
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rtt−r
12. 2v+2w1v2−1w2
13. x−2xx+31x+3+1x−3
- Answer
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(x+1)(x−3)2
14. y−2yy−42y−4+2y+4
15. 2−2a+31a+3+a2
- Answer
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4a+1
16. 4+4b−51b−5+b4
Simplify a Complex Rational Expression by Using the LCD
In the following exercises, simplify each complex rational expression by using the LCD.
17. 13+1814+112
- Answer
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118
18. 14+1916+112
19. 56+29718−13
- Answer
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19
20. 16+41535−12
21. cd+1d1d−dc
- Answer
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c2+cc−d2
22. 1m+mnnm−1n
23. 1p+1q1p2−1q2
- Answer
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pqq−p
24. 2r+2t1r2−1t2
25. 2x+53x−5+1x2−25
- Answer
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2x−103x+16
26. 5y−43y+4+2y2−16
27. 5z2−64+3z+81z+8+2z−8
- Answer
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3z−193z+8
28. 3s+6+5s−61s2−36+4s+6
29. 4a2−2a−151a−5+2a+3
- Answer
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43a−7
30. 5b2−6b−273b−9+1b+3
31. 5c+2−3c+75cc2+9c+14
- Answer
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2c+295c
32. 6d−4−2d+72dd2+3d−28
33. 2+1p−35p−3
- Answer
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2p−55
34. nn−23+5n−2
35. mm+54+1m−5
- Answer
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m(m−5)(4m−19)(m+5)
36. 7+2q−21q+2
In the following exercises, simplify each complex rational expression using either method.
37. 34−2712+514
- Answer
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1324
38. vw+1v1v−vw
39. 2a+41a2−16
- Answer
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2(a−4)
40. 3b2−3b−405b+5−2b−8
41. 3m+3n1m2−1n2
- Answer
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3mnn−m
42. 2r−91r+9+3r2−81
43. x−3xx+23x+2+3x−2
- Answer
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(x−1)(x−2)6
44. yy+32+1y−3
Writing Exercises
45. In this section, you learned to simplify the complex fraction 3x+2xx2−4 two ways: rewriting it as a division problem or multiplying the numerator and denominator by the LCD. Which method do you prefer? Why?
- Answer
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Answers will vary.
44. Efraim wants to start simplifying the complex fraction 1a+1b1a−1b by cancelling the variables from the numerator and denominator, 1a+1b1a−1b. Explain what is wrong with Efraim’s plan.