Basic Technical Mathematics, 11th Edition

Exercises 6.5, page 203

1. 1. ${\displaystyle \frac{(x\hspace{0.17em}-\hspace{0.17em}2)(x\hspace{0.17em}+\hspace{0.17em}3)}{3x\hspace{0.17em}-\hspace{0.17em}1}}$

2. 3. ${\displaystyle \frac{1}{15}}$

3. 5. 6xy

4. 7. ${\displaystyle \frac{7}{18}}$

5. 9. ${\displaystyle \frac{y^2}{b^2}}$

6. 11. ${\displaystyle \frac{2y}{5}}$

7. 13. $3(u\hspace{0.17em}+\hspace{0.17em}v)(u\hspace{0.17em}-\hspace{0.17em}v)$

8. 15. ${\displaystyle \frac{50}{3(a\hspace{0.17em}+\hspace{0.17em}4)}}$

9. 17. ${\displaystyle \frac{x^2\hspace{0.17em}-\hspace{0.17em}3}{x^2}}$

10. 19. ${\displaystyle \frac{3x}{5a}}$

11. 21. ${\displaystyle \frac{(x\hspace{0.17em}+\hspace{0.17em}1)(x\hspace{0.17em}-\hspace{0.17em}1)(x\hspace{0.17em}-\hspace{0.17em}4)}{4(x\hspace{0.17em}+\hspace{0.17em}2)}}$

12. 23. ${\displaystyle \frac{x^2}{a\hspace{0.17em}+\hspace{0.17em}x}}$

13. 25. ${\displaystyle \frac{15}{4}}$

14. 27. ${\displaystyle \frac{3(x\hspace{0.17em}-\hspace{0.17em}5)}{(x\hspace{0.17em}-\hspace{0.17em}2)(x\hspace{0.17em}+\hspace{0.17em}1)}}$

15. 29. ${\displaystyle \frac{2(3T\hspace{0.17em}+\hspace{0.17em}N)(5V\hspace{0.17em}-\hspace{0.17em}6)}{(V\hspace{0.17em}-\hspace{0.17em}7)(4T\hspace{0.17em}+\hspace{0.17em}N)}}$

16. 31. ${\displaystyle \frac{7x^4}{3a^4}}$

17. 33. ${\displaystyle \frac{4t(2t\hspace{0.17em}-\hspace{0.17em}1)(t\hspace{0.17em}+\hspace{0.17em}5)}{{(2t\hspace{0.17em}+\hspace{0.17em}1)}^2}}$

18. 35. ${\displaystyle \frac{x\hspace{0.17em}+\hspace{0.17em}y}{2}}$

19. 37. $(x\hspace{0.17em}+\hspace{0.17em}y)(3p\hspace{0.17em}+\hspace{0.17em}7q)$

20. 39. ${\displaystyle \frac{x\hspace{0.17em}-\hspace{0.17em}2}{6x}}$

21. 41. ${\displaystyle \frac{2(2x\hspace{0.17em}-\hspace{0.17em}1)}{5(2\hspace{0.17em}-\hspace{0.17em}x)}}$

22. 43. ${\displaystyle \frac{\pi }{2}}$

23. 45. ${\displaystyle \frac{c(\lambda \hspace{0.17em}+\hspace{0.17em}{\lambda }_0)(\lambda \hspace{0.17em}-\hspace{0.17em}{\lambda }_0)}{{\lambda }^2\hspace{0.17em}+\hspace{0.17em}{\lambda }_0^2}}$

24. 47. $v\hspace{0.17em}=\hspace{0.17em}\sqrt{{\displaystyle \frac{GM}{r}}}$