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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+44a2a216

Answer

a42a

2. 3bb5b2b225

3. 5c2+5c1410c+7

Answer

12(c2)

4. 8d2+9d+1812d+6

5. 12+5623+79

Answer

1213

6. 12+3435+710

7. 231934+56

Answer

2057

8. 121623+34

9. nm+1n1nnm

Answer

n2+mmn2

10. 1p+pqqp1q

11. 1r+1t1r21t2

Answer

rttr

12. 2v+2w1v21w2

13. x2xx+31x+3+1x3

Answer

(x+1)(x3)2

14. y2yy42y4+2y+4

15. 22a+31a+3+a2

Answer

4a+1

16. 4+4b51b5+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

118

18. 14+1916+112

19. 56+2971813

Answer

19

20. 16+4153512

21. cd+1d1ddc

Answer

c2+ccd2

22. 1m+mnnm1n

23. 1p+1q1p21q2

Answer

pqqp

24. 2r+2t1r21t2

25. 2x+53x5+1x225

Answer

2x103x+16

26. 5y43y+4+2y216

27. 5z264+3z+81z+8+2z8

Answer

3z193z+8

28. 3s+6+5s61s236+4s+6

29. 4a22a151a5+2a+3

Answer

43a7

30. 5b26b273b9+1b+3

31. 5c+23c+75cc2+9c+14

Answer

2c+295c

32. 6d42d+72dd2+3d28

33. 2+1p35p3

Answer

2p55

34. nn23+5n2

35. mm+54+1m5

Answer

m(m5)(4m19)(m+5)

36. 7+2q21q+2

In the following exercises, simplify each complex rational expression using either method.

37. 342712+514

Answer

1324

38. vw+1v1vvw

39. 2a+41a216

Answer

2(a4)

40. 3b23b405b+52b8

41. 3m+3n1m21n2

Answer

3mnnm

42. 2r91r+9+3r281

43. x3xx+23x+2+3x2

Answer

(x1)(x2)6

44. yy+32+1y3

Writing Exercises

45. In this section, you learned to simplify the complex fraction 3x+2xx24 two ways: rewriting it as a division problem or multiplying the numerator and denominator by the LCD. Which method do you prefer? Why?

Answer

Answers will vary.

44. Efraim wants to start simplifying the complex fraction 1a+1b1a1b by cancelling the variables from the numerator and denominator, 1a+1b1a1b. Explain what is wrong with Efraim’s plan.


This page titled 7.4E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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