- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 1 (39.63 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 2 (50.57 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 3 (27.21 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 4 (55.92 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 5 (29.68 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 6 (26.03 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 7 (34.13 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 8 (49.88 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 9 (55.68 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 10 (24.7 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 11 (19.46 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 12 (51.97 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 13 (51.97 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 14 (41.75 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 15 (40.88 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 16 (37.15 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 17 (42.28 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 18 (12.38 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 19 (15.65 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 20 (45.85 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 21 (7.89 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 22 (43.91 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 23 (47.69 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 24 (9.2 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 25 (38.39 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 26 (35.39 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 27 (14.58 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 28 (19.03 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 29 (36.47 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 30 (43.49 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 31 (45.79 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 32 (33.38 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 33 (28.84 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 34 (35.22 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 35 (27.76 KiB) Viewed 30 times
- Practice Fimeriation 16 F X T 2xir 4 A 5 19 F A V 5r23x C F X N 3x2 3 F 2 F00 F 5 12 F X X 7y2x 2 F 36 (30.23 KiB) Viewed 30 times
(41.) 3x+103x+7 69. 2a+b4a2+2ab+b2⋅8a3−b34a2−b2 42. 2x+52x+3 cannot te uimpifified 70. b2−b−627a3−8b3⋅3ac−2bc−3a+2bbc−b−3c+3b+28a2+6ab+3b2 43. 16−x2x2−x−12x+4x+3 44. 9−x2x2−7x+12−x+31−4 71. 3z2−8z+510z2+13z−3⋅25z2−10z+12z2−3z−2z+3⋅4z2−915z2−28z+5 45. 3x2−7xy+2y2x2+3xy−10y23x−46x+5y−y2x2+5xy−3y2x2+2xy−3y22x−yx−y 72. z2−492z2−2z−12⋅2z2+5z+24z2−1⋅2z2−7z+32z2−13z−7z+722z+11 (47. x2−4x3−8x+2x2+2x+4 48. x2−1x3−1x+1x2+x+1 In Exercises 73-90, divide as indicated. 49. x+4x3+4x2−3x−12x2−3 73. 7x+5÷94x+20244 74. 3x+1÷73x+341 50. x−2x3−2x2+x−2,x2+1 75. y−64+7y−4240107 76. y−57+3y−1528 77. 15x2−2x+5x−2 78. 15x2−x÷5x−1 SECTION 6.1 Rational Expressions and Functions: Multiplying and Dividing 415 62. (x2+4x−5)+x+7x2−25x−3(x+7x−1) 103. Find (gf)(x) and the domain of gf, 62 y2−10y+25y2−4y−21+y2−6y+5y2+2y−3y−y−4y−7 (fR)(x)=−1−2(−8,−2)∪(−2,1)∪(f,=) 64. y2+3y−28y2+4y−21+y2+4y−32y2+14y+48y+6z−3 104. Find (fg)(x) and the domain of fg 85. 4x2+2x+18x3−1÷(x−1)2x−1(x−1)(2x−1) (f1)(x)=−x+221−x−22(−∞,−2)∪(−2,f)∪(f,−1)1 66. x3−27x2−9÷x2+3x+9x2+6x+9x+31 (67. x2+3xy+2y2x2−4y2+x+yx2−4xy+4y2x−2y1 Application Exercises The rational function
Practice Exercises In Exercises 1-l6, perform the indicated operations. These 8. y2−25y2+y2−2525−10yy+5y−5 exercises imvolve addition and subsraction when denominators are the same. Simplify the result, if possible. 9. 4x−33x−4x−32x−14x−1x+1 1. 9x2+9x43x2 10. 7x−43x−7x−42x−17x−4x+1 2. 6x11+6x4215 (11) x2+6x−7x2−2−x2+6x−719−4xx−11 (3.) x−5x+x−59x+3x−511x+3 12. x2+x−6x2+6x+2−x2+x−62x−1xx+1−2 4. x−3x+x−311x+5x−112x+5 13. 6y2+y−220y2+5y+1−6y2+y−28y2−12y−524y+1+1 5. x2+3xx2−2x+x2+3xx2+xx+x2x−1 14. y2−5y+4y2+3y−6−y2−5y+44y−4−2y23+2 6. x2−5xx2+7x+x2−5xx2−4x1−52x+3 15. x2−y22x3−3y3−x2−y2x3−2y3y3+x+y+y3 (7.) y2−9y2+y2−99−6yy−3 16. y2−x24y3−3x3−y2−x23y3−2x3y2+xy+y2
It Exrcises 17-28, find the leas common denominator of the. nalionad expresaione: 39. y2−5y+63y+7−y−336−5(y−2)11 (7) 25x211 and 35x14 40. y2−7y+122y+9−y−32(y−3)(y−4)11 12. 15x27 and 24x9 41. x2+9x+18x2−6−x+6x−4+1 19. x−52 and x2−253(x−5)(x+5) 42. x2+3x−10x2−39−x−2x−7=x+32 20. x+32 and x2−95(1+3x+−3) (43.) x2+7x+124x+1+x2+5x+42x+3(1+1kx+4x+3)6x2+14x+10 21. y2−1007 and y(y−10)13y(x+10)(y−10) 44. x2−x−63x−2+x2−94x−34+3(x−3)(x+2)72+12x−12 22. y2−47 and y(y+2)15 45. x2−x−2x+4−x2+2x−82x+3−(0+4x+2kx+1)x2−1x−13 23. x2−168 and x2−8x+16x(x+4)(x−4)(x−4) 46. x2−7x+62x+1−x2−5x−6x+3(x−5)(x+1)(x−1)y3+x+4 24. x2−253 and x2−10x+25x(x+5)(x−5)(x−5) 47. 4+x−31x−34x−11 (25.) y2−5y−6 and y2−4y−5y(y−5)(y−6)(y+1) 48. 7+x−51x−57x−4 27. 2y2+7y+67y,y2−43 and 2y2−3y−2−7y 49. y2−16y−7+16−y27−y(y+4)(y−4)2y−14 50. y2−25y−3+25−y2y−3 28. y2−95y,y2+6y+98, and 2y2+5y−3−5y 51. 3x+6x+7+4−x2xx(x+2x−2)x2+2x−14 In Exercises 20-66, perform the indicated operations, These 52. 4x+12x+5+9−x2x4(5−1)4−3 etercises involve adduition and subtraction when denominators are different. Simplify the reselt, if possible. (53) x−42x+x2−1664−x+42x=x−416 (20) 5x23+x104x23+51x 54. x−3x+x2−2x−3x+2−x+14x+16x−3yx2−2x+14 30. 2x27+x4x27+xr 55. x2−y25x−y−x7x2−y213x+7y 31. x−24+x+13(x−2)(x+1)7x−2 56. x2−y29x−y−x10x2−y218x+10y 32. x−32+x+27(0−3)(x+2) (57) 5x+63−x−24+5x2−4x−12x2−x84+6(x−2)x2−the−30 33. x2+x−23x+x2−4x+32(x+2xx−113x−4 58. x2+2x+1x−1−2x−23+x2−1x2x+16x+1)(x−1x2−16−1 34. x2+2x−87x+x2−3x+23(x+4)(x−2)(x−1) 59. x2−9xy+20y23x−y+x2−25y22y(1+5,4x−5,4x−4x2+1e2) 35. x+5x−6+x−6x+5(1+5)(x−6)2x2−2x+6) 36. x+7x−2+x−2x+711+7hx−21x2+16x+53 60. x2+4xy+4y2x+2y−x2−4y22x−x−2y1 61. x2−43x+x2+x−25x−x2−4x+43
Practice Exercises In Exercises 1−40, simplify each complex rational expression by the method of your choice. 11. 5x+51−x1−x(x+5)1 12. 6x+61−x1−x(x+6)1 (1.) 1−x34+x21−341+2 2. 3+x15−x23+15x−2 13. x+41−x1x+44 14. x+71−x1x+77 3. 3x−x3x3+3x(x−3)(x+3)x2+4 4. 51+x15x−x5,=5 15. x+11−1x−11+1−x−11 16. x−11+1x+11−1−x+1x−1 (5.) x1−y1x1+y1y−1y+1 17. (x+y)−1x−1+y−1xy(4+y(x+y) 6. xy+x1yx+x1x+11x2+y 18. (x−1+y−1)−11+yxy 7. 10x−1−6x−28x−2−2x−15x−34−x 8. 15x−1−9x−212x−2−3x−14x−34−x 19. x+2x−2+x−2x+2x−2x+2−x+2x−2 20. x+1x+1+x−1x+2x−1x+1−x+1x−1x2x2+x+3 9. 1−x−21x−21x−31 10. 1+x+21x+21+1+11 21. x3y5−xy3x3y2+xy45 (4) 22. x2y1+xy32xy23+x2y2
30. y−33+y−22y2−5y+65y sy 31. a21−ab3+b22+2x−20a22−ab1−b21 45. 1−1+x111 35. x2+2xy3y+x5x+2y3−x2+2xy2y13y+3414−2y In Exerises 47−48, fet f(x)=1−x1+x, 47. Find f(x+31) and simplify. x+2x+4 48. Find f(x−61) and simplify. := ? 36. x−y1−x2+xy+y21x3−y31y2+x+y2−1+y1 In Exercises 49-50, use the given rational function to find and simplify 37. m2−12+m2+4m+3m(m+3)m2−m−22m2−3m+2(m−2)m−2nm+11 hf(a+h)−f(a)
Practice Exercises In Exercises 13-36, divide as indicated. Check at least five of In Exercises 1-12, divide the polynomial by the monountal. Your answers by showing that she product of the divisor and the (1. 5x325x7−15x5+10x35x4−x2+2 (13.) (x2+8x+15)+(x+5)=3 2. 7x349x7−28x5+14x3−7x4−4x2+2 14. (x2+3x−10)+(x−2)+5 3. 3x18x3+6x2−9x−6x2+2x−3−42 15. (x3−2x2−5x+6)÷(x−3)x2+x−2 4. 5x25x3+50x2−40x−10+x2+60x−8−x2 16. (x3+5x2+7x+2)+(x+2)x2+34+1 (5.) (28x3−7x2−16x)+(4x2)+7−47−14 17. (x2−7x+12)÷(x−5)x−2+x−52 6. (70x3−10x2−14x)+(7x2) ine −710−22 18. (2x2+x−9)÷(x−2)2x+5+x−21 7. (25x8−50x7+3x6−40x5)+(−5x5) 19. (2x2+13x+5)+(2x+3)+5−2x+316 −5x2+40x2−53x+3 20. (8x2+6x−25)+(4x+9)2x−3+4r+92 8. (18x7−9x6+20x5−10x4)÷(−2x4) 21. (x3+3x2+5x+4)+(x+1)x3+2x+3+x+11 −9x3+24x7−16x+5 22. (x3+6x2−2x+3)+(x−1)x2+7x+5+x−15 9. (18a3b2−9a2b−27ab2)÷(9ab)≥a2b−a−16 23. (4y3+12y2+7y−3)+(2y+3)2y2+3y−1 10. (12a2b2+6a2b−15ab2)+(3ab)ab+2a−5b 24. (6y3+7y2+12y−5)+(3y−1)2y2+3y+5 25. (9x3−3x2−3x+4)+(3x+2) 342−3+1+162+3
49. x−3y4x3−7x3y−16ay2+3y3 6r +40y 34. (4y4−17y2+14y−3)+(2y−3)+2y4+1y−2+4+1 60. 4x−5y12x3−19x2y+13ry2−10y3 (33. (4x4+3x3+4x2+9x−6)+(x2+3) In Euercites 51-52 fond (hf−g)(x) and the donnain of 34. (3x3−x1+4x2−12x−8)+(x2−2) 51. f(x)=3x3+4x2−x−4.(x)=−5x3+22x2−24x−2x 35. (15x4+3x3+4x2+4)+(3x2−1)+3x1+x+3+8+7 3n 52. f(x)=x3+9x2−6x+25,5(x)=−3x3+2x2−14x 37. f(x)=8y3−38x2+49x−10. simplify. 54. ax −3x+6=a3−6a2+11ay=e2−40−2 33. f(x)=2x3−9x2−17x+39. g(x)=2x−3(1)(n=1+−4−13 Application Exercises 39. f(x)=2x4−7x3+7x2−9x+10, g(x)=2x−5(f)(x)=,x′+x−2f(x)=x−11080t−800,300x≤100 Rewrite the function by using long division to perfort 44. x2−3x−2x4−x3−7x2−7x−2 you obtain the same answer as you did in Excrioe Which form of the functioa do you find eacer to you obtain the same answet as yoe did in 1 setcoe Which form of the functioa do yow find easicr to ese"
wo ciercises, begin the provess as shown. 26. f(x)=6x4+10x3+5x2+x+1 : f(−32) 4. (5x2−12x−8)+(x+3)-x −27=7 5. (4x3−3x2+3x−1)+(x−1) 4x- * s 6. (5x3−6x2+3x+11)+(x−2) 7. (6x3−2x3+4x2−3x+1)÷(x−2) (27) x3−4x2+x+6=0,−1 8. (x3+4x4−3x2+2x+3)+(x−3) 29. 2x3−5x2+x+2=0,2 x4+7x3+21v2+ ARA =1ke+1−734 30. 2x3−3x2−11x+6=0x−2 2. (x2−5x−5x3+x4)+(5+x) (31) 6x3+25x2−24x+5=0x−5 32. 3x3+7x2−22x−8=0;−4 pot'momial equation (17) (3x3+2x2−4x+1)+(x−31)42+3x−3 12. (2x4−x3+2x2−3x+1)+(x−21)≥x+2x−5= 12. x−1x4+x3−2y2+y2+y4+2y+2 14. x+2x7+x5−10x3+12 33. x3+2x2−5x−6=0 (15) x−4x4−256+2 *r + is =14 34. 2x3+x2−13x+6=0 17. x+22x5−3x4+x3−x2+2x−1 18. x−2x3−2x4−x3+3x2−x+1+x4−x2+x+1+x−23
In Exercises 1-34, solve each rational equation. If an equation has no solution, so state. 12. x−43x+1=2x−76x+5 ne sulatiin of Q 1. x1+2=x3 (13.) 1−x+74=x+75 14. 5−x−52=x−53 2. x1−3=x4∣−1∣ 15. x+24x+x−12=4 ∣2∣} 3. x5+31=x6 16. x+13x+x−24=3 |-10| 4. x4+21=x5 17. x2−98+x+34=x−32 (5.) 2xx−2+1=xx+1 18. x2−2532=x+54+x−52 (31) 6. 5x7x−4=59−x4 19. x+x7=−8∣−7,−1∣ 7. x+13=x−15∣−4∣ 20. x+x6=−7∣−6,−1∣ 8. x+36=x−34 [15] (21.) x6−3x=1(−6,3) 9. x+5x−6=x+1x−3 22. 2x−x12=1(−4,0)
(25) x−11+x+11=x2−12 nen solation or 2 46. x3−12+(x−1)(x2+x+1)4+x2+x+11 26. x−21+x+21=x2−44 eosinuser or Q (31.) x+45+x+33=x2+7x+1212x+19 In Exercises 47-48, find all values of a for which 29. x2+2x−82x−1+x+42=x−21 f(a)=g(a)+1. 47. f(x)=x+3x+2,g(x)=x2+2x−3x+1 29. x+34x−x−312=x2−94x2+36 48. f(x)=x−34⋅g(x)=x4+x−1210−1,6 30. x+32−x+15=x2+4x+33x+5 In Exercises 49−50, find all values of a for which or is (31) x2+3x−104+x2+9x+201=x2+2x−82(43) (f+g)(a)=h(a). 49. f(x)=x−45,g(x)=y−x3,h(x)=x2−7x+13x2−20
(1.) f(x)=x+3x2−9;f(−2),f(0),f(5) 2. f(x)=x+4x2−16;f(−2),f(0),f(5) 3. f(x)=4−xx2−2x−3;f(−1),f(4),f(6) 4. f(x)=3−xx2−3x−4;f(−1),f(3),f(5) 5. g(t)=t2+12t3−5;g(−1),g(0),g(2) 6. g(t)=t2+42t3−1;g(−1),g(0),g(2) In Exercises 7-16, find the domain of the given rational function. 7. f(x)=x−5x−2
11. f(x)=(x+5)22x 12. f(x)=(x+7)22x 13. f(x)=x2−8x+153x 14. f(x)=x2−13x+363x 15. f(x)=3x2−2x−8(x−1)2
In Exercises 27-50, simplify each rational expression. If the rational expression cannot be simplified, so state. 27. x−2x2−4 28. x−5x2−25 29. x2−x−6x+2 30. x2−2x−3x+1 31. x2+5x4x+20 32. x2+6x5x+30 33. y2−254y−20 34. y2−496y−42 35. 25−9x23x−5 36. 4−25x25x−2 37. y2−14y+49y2−49 38. y2−6y+9y2−9 39. x2−3x+2x2+7x−18 40. x2+5x+4x2−4x−5 41. 3x+103x+7 42. 2x+52x+3 43. 16−x2x2−x−12 44. 9−x2x2−7x+12 45. 3x2−7xy+2y2x2+3xy−10y2 46. 2x2+5xy−3y2x2+2xy−3y2 47. x2−4x3−8 48. x2−1x3−1
In Exercises 51-72, multiply as indicated. 51. x+7x−3⋅2x−63x+21 52. x+3x−2⋅5x−102x+6 53. x2−4x−21x2−49⋅xx+3 54. x2−3x−10x2−25⋅xx+2 55. x2−x−6x2−9⋅x2+x−6x2+5x+6 56. x2−4x2−1⋅x2−2x−3x2−5x+6 57. x2+8x+16x2+4x+4⋅(x+2)3(x+4)3 58. x2−4x+4x2−2x+1⋅(x−1)3(x−2)3 59. y2−98y+2⋅4y2+y3−y 60. y2−16y+2⋅3y2+y1−y 61. y2−4y3−8⋅2yy+2 62. y3+27y2+6y+9⋅y+31 63. (x−3)⋅x2−5x+6x2+x+1 64. (x+1)⋅x2+7x+6x+2 65. x2−y2x2+xy⋅x4x−4y fr x2−y2x2+xy
69. 2a+b4a2+2ab+b2⋅8a3−b34a2−b2 70. b2−b−627a3−8b3⋅3ac−2bc−3a+2bbc−b−3c+3 71. 3z2−8z+510z2+13z−3⋅25z2−10z+12z2−3z−2z+3⋅4z2−915z2−28z 72. z2−492z2−2z−12⋅2z2+5z+24z2−1⋅2z2−7z+32z2−13z−7 In Exercises 73-90, divide as indicated. 73. 7x+5÷94x+20 74. 3x+1÷73x+3
87. x2+3xy+2y2x2−4y2÷x+yx2−4xy+4y2
In Exercises 103-104, let f(x)=1−2x(x+2)2 and g(x)=2x−1−x+2. 103. Find (gf)(x) and the domain of gf.
6.2 EXERCISE SET MyMathLab Practice Exercises In Exercises 1-16, perform the indicated operations. These exercises involve addition and subtraction when denominators are the same. Simplify the result, if possible. 1. 9x2+9x4 2. 6x11+6x4 3. x−5x+x−59x+3 4. x−3x+x−311x+5 5. x2+3xx2−2x+x2+3xx2+x 6. x2−5xx2+7x+x2−5xx2−4x 7. y2−9y2+y2−99−6y
(11.) x2+6x−7x2−2−x2+6x−719−4x
In Exercises 17-28, find the least common denominator of the rational expressions. (17.) 25x211 and 35x14 18. 15x27 and 24x9 19. x−52 and x2−253 20. x+32 and x2−95 21. y2−1007 and y(y−10)13 22. y2−47 and y(y+2)15 23. x2−168 and x2−8x+16x 24. x2−253 and x2−10x+25x 25. y2−5y−67 and y2−4y−5y
In Exercises 29-66, perform the indicated operations. These exercises involve addition and subtraction when denominators are different. Simplify the result, if possible. 29. 5x23+x10 30. 2x27+x4 31. x−24+x+13 32. x−32+x+27 33. x2+x−23x+x2−4x+32 34. x2+2x−87x+x2−3x+23 35. x+5x−6+x−6x+5 36. x+7x−2+x−2x+7 37. x2−253x−x+54
43. x2+7x+124x+1+x2+5x+42x+3
53. x−42x+x2−1664−x+42x 54. x−3x+x2−2x−3x+2−x+14 55. x2−y25x−y−x7 56. x2−y29x−y−x10 57. 5x+63−x−24+5x2−4x−12x2−x
In Exercises 1-40, simplify each complex rational expression by the method of your choice. 1. 1−x34+x2 2. 3+x15−x2 3. 3x−x3x3+3x 4. 51+x15x−x5 (5. x1−y1x1+y1 6. xy+x1yx+x1 7. 10x−1−6x−28x−2−2x−1 8. 15x−1−9x−212x−2−3x−1 9. 1−x−21x−21 10. 1+x+21x+21
x3y5−xy3x3y2+xy45
y+31+y+12y2+4y+32y
In Exercises 47-48, let f(x)=1−x1+x. 47. Find f(x+31) and simplify. 48. Find f(x−61) and simplify. In Exercises 49-50, use the given rational function to find and simplify hf(a+h)−f(a) 49. f(x)=x3
Practice Exercises In Exercises 1-12, divide the polynomial by the monomial. (1.) 5x325x7−15x5+10x3 2. 7x349x7−28x5+14x3 3. 3x18x3+6x2−9x−6 4. 5x25x3+50x2−40x−10 5. (28x3−7x2−16x)÷(4x2) 6. (70x3−10x2−14x)÷(7x2) 7. (25x8−50x7+3x6−40x5)÷(−5x5) 8. (18x7−9x6+20x5−10x4)÷(−2x4) 9. (18a3b2−9a2b−27ab2)÷(9ab)
In Exercises 13-36, divide as indicated. Check at least five of your answers by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. 13. (x2+8x+15)÷(x+5) 14. (x2+3x−10)÷(x−2) 15. (x3−2x2−5x+6)÷(x−3) 16. (x3+5x2+7x+2)÷(x+2) 17. (x2−7x+12)÷(x−5) 18. (2x2+x−9)÷(x−2) 19. (2x2+13x+5)÷(2x+3) 20. (8x2+6x−25)÷(4x+9) 21. (x3+3x2+5x+4)÷(x+1) 22. (x3+6x2−2x+3)÷(x−1) 23. (4y3+12y2+7y−3)÷(2y+3) 24. (6y3+7y2+12y−5)÷(3y−1) 25. (9x3−3x2−3x+4)÷(3x+2)
29. (4y3−5y)÷(2y−1) 30. (6y3−5y)÷(2y−1) 31. (4y4−17y2+14y−3)÷(2y−3) 32. (2y4−y3+16y2−4)÷(2y−1) 33. (4x4+3x3+4x2+9x−6)÷(x2+3)
Practice PLUS In Exercises 41-50, divide as indicated. 41. x+yx4+y4 42. x+yx5+y5 43. x2+x+23x4+5x3+7x2+3x−2 44. x2−3x−2x4−x3−7x2−7x−2 45. x2+x+14x3−3x2+x+1 46. x2+x+1x4−x2+1 47. x2−x+2x5−1
MyMathLab° Practice Exercises In Exercises 1-18, divide using synthetic division. In the first two exercises, begin the process as shown. 1. (2x2+x−10)÷(x−2)221−10 2. (x2+x−2)÷(x−1) 1] 1 1 −2 3. (3x2+7x−20)÷(x+5) 4. (5x2−12x−8)÷(x+3) 5. (4x3−3x2+3x−1)÷(x−1) 6. (5x3−6x2+3x+11)÷(x−2) 7. (6x5−2x3+4x2−3x+1)÷(x−2) 8. (x5+4x4−3x2+2x+3)÷(x−3) 9. (x2−5x−5x3+x4)÷(5+x) 10. (x2−6x−6x3+x4)÷(6+x) 11. (3x3+2x2−4x+1)÷(x−31) 12. (2x4−x3+2x2−3x+1)÷(x−21) 13. x−1x5+x3−2 14. x+2x7+x5−10x3+12 15. x−4x4−256
In Exercises 19-26, use synthetic division and the Remainder Theorem to find the indicated function value. 19. f(x)=2x3−11x2+7x−5;f(4) 20. f(x)=x3−7x2+5x−6;f(3) 21. f(x)=3x3−7x2−2x+5;f(−3) 22. f(x)=4x3+5x2−6x−4;f(−2) 23. f(x)=x4+5x3+5x2−5x−6;f(3) 24. f(x)=x4−5x3+5x2+5x−6;f(2)
In Exercises 27-32, use synthetic division to show that the number given to the right of each equation is a solution of the equation. Then solve the polynomial equation. 27. x3−4x2+x+6=0;−1 28. x3−2x2−x+2=0;−1 29. 2x3−5x2+x+2=0;2 30. 2x3−3x2−11x+6=0;−2 31. 6x3+25x2−24x+5=0;−5