By Madison, Wis., 1973 Advanced Seminar on Generalized Inverses and Applications, M. Zuhair Nashed

ISBN-10: 0125142501

ISBN-13: 9780125142502

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6x 2 6. 3y 4 7. x2 ϩ x Ϫ 2 x 2 ϩ 3x ϩ 2 18y 2 12m Ϫ 6 18m Ϫ 9 8y 2 4y 3 Ϫ 4y 2 ϩ 8y 9. 11. x2 Ϫ 4 2x 2 Ϫ x Ϫ 6 x3 ϩ y3 x Ϫ xy ϩ y 2 2 8. 10. 12. 4 RATIONAL EXPRESSIONS In Exercises 13–46, perform the indicated operations and simplify. 13. 15. 6x 3 32 3x # 8 3x 3 8x 2 Ϭ 3x 17. x ϩ 2y 14. 2 15x 4 16. 16x 5 # 22. 23. 24. 25. 27. 28. 29. 30. 6r 2 Ϫ r Ϫ 2 2r ϩ 4 k ϪkϪ6 # 2x2 2 Ϭ 4 x Ϫ9 2 Ϫ 35. 3y Ϫ 6 6y ϩ 24 20. Ϭ 4y ϩ 6 8y ϩ 12 36. 37. ϪxϪ6 y ϩ y Ϫ1 2 x x ϩ 5x ϩ 6 2x ϩ 1 2x 2 Ϫ x Ϫ 1 ϩ Ϫ 2 x Ϫ4 2 26.

2k 2 Ϫ 4 ϭ 4 Ϫ k 36. 24k 2 Ϫ 3 ϭ 2k ϩ 1 37. 2k ϩ 1 ϩ 2k ϭ 3 2k 38. 2x ϩ 1 Ϫ 2x ϭ 24x Ϫ 3 In Exercises 39–46, solve the equation for the indicated variable. 39. I ϭ Prt; r 40. ax ϩ by ϩ c ϭ 0; y 41. p ϭ Ϫ3q ϩ 1; q s2 ;u ax ;x xϩb 44. V ϭ C a 1 Ϫ 2mI ;m B1n ϩ 12 46. r ϭ 43. V ϭ 45. r ϭ 42. w ϭ ku√ n b; n N 2mI ;n B1n ϩ 12 47. SIMPLE INTEREST The simple interest I (in dollars) earned when P dollars is invested for a term of t yr is given by I ϭ Prt, where r is the (simple) interest rate/year. Solve for t in terms of I, P, and r.

Factor this expression. 2 4 35. (a Ϫ 2b)2 Ϫ (a ϩ 2b)2 Factor this expression. 3 36. 2x(x ϩ y)2 Ϫ 8x(x ϩ y 2)2 58. 1x 2 ϩ 500x dollars. Factor the expression on the right-hand side of this equation. 3 Solutions to Self-Check Exercises 1. a. The common factor is 2x 2. Therefore, b. We first factor out the common factor 2. Thus, 4x 2 ϩ 10x Ϫ 6 ϭ 2(2x 2 ϩ 5x Ϫ 3) 4x Ϫ 2x ϭ 2x (2x Ϫ 1) 3 2 2 b. The common factor is a2 ϩ 2b2. Therefore, 3(a ϩ 2b ) ϩ 4(a ϩ 2b ) ϭ (a ϩ 2b )[3 ϩ 4(a ϩ 2b )] 2 2 2 2 2 2 2 2 2 ϭ (a2 ϩ 2b2)(3 ϩ 4a2 ϩ 8b2) 2.

### Generalized inverses and applications: proceedings of an advanced seminar by Madison, Wis., 1973 Advanced Seminar on Generalized Inverses and Applications, M. Zuhair Nashed

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