Practice and Problem-Solving Exercises

A Practice

See Problems 1, 2, and 3.

Simplify each expression. State any excluded values.

8. 6 a + 9 12 fraction 6 eh plus 9 , over 12 end fraction
9. 4 x 3 28 x 4 fraction 4 , x cubed , over 28 , x to the fourth end fraction
10. 2 m − 5 6 m − 15 fraction 2 m minus 5 , over 6 m minus 15 end fraction
11. 2 p − 24 4 p − 48 fraction 2 p minus 24 , over 4 p minus 48 end fraction
12. 3 x 2 − 9 x x − 3 fraction 3 , x squared , minus 9 x , over x minus 3 end fraction
13. 3 x + 6 3 x 2 fraction 3 x plus 6 , over 3 , x squared end fraction
14. 2 x 2 + 2 x 3 x 2 + 3 x fraction 2 , x squared , plus 2 x , over 3 , x squared , plus 3 x end fraction
15. 2 b − 8 b 2 − 16 fraction 2 b minus 8 , over b squared , minus 16 end fraction
16. m + 6 m 2 − m − 42 fraction m plus 6 , over m squared , minus m minus 42 end fraction
17. w 2 + 7 w w 2 − 49 fraction w squared , plus 7 w , over w squared , minus 49 end fraction
18. a 2 + 2 a + 1 5 a + 5 fraction eh squared , plus 2 eh plus 1 , over 5 eh plus 5 end fraction
19. m 2 + 7 m + 12 m 2 + 6 m + 8 fraction m squared , plus 7 m plus 12 , over m squared , plus 6 m plus 8 end fraction
20. c 2 − 6 c + 8 c 2 + c − 6 fraction c squared , minus 6 c plus 8 , over c squared , plus c minus 6 end fraction
21. b 2 + 8 b + 15 b + 5 fraction b squared , plus 8 b plus 15 , over b plus 5 end fraction
22. m + 4 m 2 + 2 m − 8 fraction m plus 4 , over m squared , plus 2 m minus 8 end fraction
23. 5 − 4 n 4 n − 5 fraction 5 minus 4 n , over 4 n minus 5 end fraction
24. 12 − 4 t t 2 − 2 t − 3 fraction 12 minus 4 t , over t squared , minus 2 t minus 3 end fraction
25. 4 m − 8 4 − 2 m fraction 4 m minus 8 , over 4 minus 2 m end fraction
26. m − 2 4 − 2 m fraction m minus 2 , over 4 minus 2 m end fraction
27. v − 5 25 − v 2 fraction v minus 5 , over 25 minus , v squared end fraction
28. 4 − w w 2 − 8 w + 16 fraction 4 minus w , over w squared , minus 8 w plus 16 end fraction

    See Problem 4.

29. Geometry The length of a rectangular prism is 5 more than twice the width w. The volume of the prism is 2 w 3 + 7 w 2 + 5 w . 2 , w cubed , plus 7 , w squared , plus 5 w .  What is a simplified expression for the height of the prism?
30. Geometry Rectangle A has length 2 x + 6 2 x plus 6  and width 3x. Rectangle B has length x + 2 x plus 2  and an area 12 square units greater than Rectangle A's area. What is a simplified expression for the width of Rectangle B?

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