Ejercicio 142

CAPITULO XV

Ecuaciones fraccionarias de primer grado
Resolución de ecuaciones fraccionarias con denominadores compuestos
Ejercicio 142
Resolver las siguientes ecuaciones
  1. 3 5 + 3 2x1 =0 3(2x1 ) +3( 5 ) 5(2x1 ) =0 6x3+15 =0 6x+12 =0 6x =12 x = 6 x =2
  2. 2 4x1 = 3 4x+1 2(4x+1 ) =3(4x1 ) 8x+2 =12x3 8x12x =32 4x =5 x = 5 4
  3. 5 x 2 1 = 1 x1 5 (x1 )(x+1 ) = 1 x1 5 x+1 =1 5 =x+1 51 =x x =4
  4. 3 x+1 1 x 2 1 =0 3 x+1 = 1 x 2 1 3 x+1 = 1 (x+1 )(x1 ) 3 = 1 x1 3(x1 ) =1 3x3 =1 3x =1+3 3x =4 x = 4 3
  5. 5x+8 3x+4 = 5x+2 3x4 (5x+8 ) (3x4 ) =(5x+2 ) (3x+4 ) 15 x 2 20x+24x32 = 15 x 2 +20x+6x+8 4x =26x+8+32 4x26x =40 22x =40 x = x = 20 11
  6. 10 x 2 5x+8 5 x 2 +9x19 =2 10 x 2 5x+8 =2(5 x 2 +9x19 ) 10 x 2 5x+8 = 10 x 2 +18x38 5x18x =388 23x =46 x = 23 x =2
  7. 1 3x3 + 1 4x+4 = 1 12x12 1 3(x1 ) + 1 4(x+1 ) = 1 12(x1 ) 4(x+1 ) +3(x1 ) 12(x1 ) (x+1 ) = 1 12(x1 ) 4(x+1 ) +3(x1 ) x+1 =1 4x+4+3x3 =x+1 7x+ 1 =x+ 1 7xx =0 6x =0 x =0
  8. x 4 x 2 8x 4x5 = 7 4 x(4x5 ) 4( x 2 8x ) 4 (4x5 ) = 7 4 4 x 2 5x 4 x 2 +32x =7(4x5 ) 27x =28x35 27x28x =35 x =35 x =35
  9. 2x9 10 + 2x3 2x1 = x 5 (2x9 ) (2x1 ) +10(2x3 ) (2x1 ) = x 5 (2x9 ) (2x1 ) +10(2x3 ) =2x(2x1 ) 4 x 2 2x 18x +9+ 20x 30 = 4 x 2 2x 21 =2x x = 21 2 x =10 1 2
  10. (3x1 ) 2 x1 = 18x1 2 2(9 x 2 6x+1 ) =(x1 ) (18x1 ) 18 x 2 12x+2 = 18 x 2 x18x+1 12x =19x+12 19x12x =1 7x =1 x = 1 7
  11. 2x+7 5x+2 2x1 5x4 =0 (2x+7 ) (5x4 ) (2x1 ) (5x+2 ) (5x+2 ) (5x4 ) =0 10 x 2 8x+35x28(10 x 2 +4x5x2 ) =0 10 x 2 +27x28 10 x 2 +x+2 =0 28x26 =0 28x =26 x = x = 13 14
  12. (5x2 ) (7x+3 ) 7x(5x1 ) 1 =0 (5x2 ) (7x+3 ) 7x(5x1 ) =1 (5x2 ) (7x+3 ) =7x(5x1 ) 35 x 2 +15x14x6 = 35 x 2 7x x+7x =6 8x =6 x = x = 3 4
  13. 3 x4 = 2 x3 + 8 x 2 7x+12 3 x4 2 x3 = 8 x 2 7x+12 3(x3 ) 2(x4 ) (x4 ) (x3 ) = 8 (x4 ) (x3 ) 3x92x+ 8 = 8 x =9
  14. 6x1 18 3(x+2 ) 5x6 = 1+3x 9 (6x1 ) (5x6 ) 54(x+2 ) (5x6 ) = 1+3x 9 30 x 2 36x5x+654x108 2(5x6 ) =1+3x 30 x 2 95x102 =2(5x6 ) (1+3x ) 30 x 2 95x102 =2(5x+15 x 2 618x ) 30 x 2 95x102 =2(15 x 2 13x6 ) 30 x 2 95x102 = 30 x 2 26x12 95x+26x =10212 69x =90 x = x = 30 23 1 7 23
  15. 5 1+x 3 1x 6 1 x 2 =0 5 1+x 3 1x = 6 1 x 2 5(1x ) 3(1+x ) (1x ) (1+x ) = 6 1 x 2 55x33x =6 28x =6 8x =62 8x =4 x = 4 x = 1 2
  16. 1+2x 1+3x 12x 13x = 3x14 19 x 2 (1+2x ) (13x ) (12x ) (1+3x ) (1+3x ) (13x ) = 3x14 19 x 2 13x+2x6 x 2 (1+3x2x6 x 2 ) =3x+14 1 x 6 x 2 1 x+ 6 x 2 =3x+14 2x =3x+14 2x+3x =14 x =14
  17. 3x1 x 2 +7x+12 = 1 2x+6 + 7 6x+24 3x1 (x+4 ) (x+3 ) = 1 2(x+3 ) + 7 6(x+4 ) 3x1 (x+4 ) (x+3 ) = 3(x+4 ) +7(x+3 ) 6 (x+4 ) (x+3 ) 6(3x1 ) =3x+12+7x+21 18x6 =10x+33 18x10x =33+6 8x =39 x = 39 8 4 7 8
  18. 1 (x1 ) 2 3 2x2 = 3 2x+2 1 (x1 ) 2 = 3 2x2 3 2x+2 1 (x1 ) 2 = 3 2(x1 ) 3 2(x+1 ) 1 (x1 ) 2 = 3(x+1 ) 3(x1 ) 2 (x1 )(x+1 ) 1 x1 = 3x +3 3x +3 2(x+1 ) 2(x+1 ) =6(x1 ) 2x+2 =6x6 2x6x =62 4x =8 x = 4 x =2
  19. 5x+13 15 4x+5 5x15 = x 3 5x+13 15 4x+5 5(x3 ) = x 3 (x3 ) (5x+13 ) 3(4x+5 ) (x3 ) = x 3 5 x 2 +13x15x3912x15 5(x3 ) =x 5 x 2 14x54 =5x(x3 ) 5 x 2 14x54 = 5 x 2 15x 15x14x =54 x =54
  20. 2x1 2x+1 x4 3x2 = 2 3 (2x1 ) (3x2 ) (x4 ) (2x+1 ) (2x+1 ) (3x2 ) = 2 3 6 x 2 4x3x+2(2 x 2 +x8x4 ) (2x+1 ) (3x2 ) = 2 3 6 x 2 7x +22 x 2 + 7x +4 (2x+1 ) (3x2 ) = 2 3 4 x 2 +6 (2x+1 ) (3x2 ) = 2 3 3. 2 (2 x 2 +3 ) = 2 (2x+1 ) (3x2 ) 6 x 2 +9 = 6 x 2 4x+3x2 9+2 =x 11 =x x =11
  21. 4x+3 2x5 3x+8 3x7 =1 (4x+3 ) (3x7 ) (3x+8 ) (2x5 ) (2x5 ) (3x7 ) =1 12 x 2 28x+9x21(6 x 2 15x+16x40 ) =(2x5 ) (3x7 ) 12 x 2 19x216 x 2 x+40 =6 x 2 14x15x+35 6 x 2 20x+19 = 6 x 2 29x+35 29x20x =3519 9x =16 x = 16 9 1 7 9
  22. 10x7 15x+3 = 3x+8 12 5 x 2 4 20x+4 10x7 3(5x+1 ) = 3x+8 12 5 x 2 4 4(5x+1 ) 10x7 3 (5x+1 ) = (5x+1 ) (3x+8 ) 3(5 x 2 4 ) (5x+1 ) 4(10x7 ) = 15 x 2 +40x+3x+8 15 x 2 +12 40x28 =43x+20 40x43x =20+28 3x =48 x = 3 x =16
  23. 4x1 5 + x2 2x7 = 8x3 10 1 3 10 (4x1 ) (2x7 ) +5(x2 ) 5(2x7 ) = 8x3 10 13 10 8 x 2 28x2x+7+5x10 5 (2x7 ) = 8x313 8 x 2 25x3 2x7 = 8x16 2 8 x 2 25x3 2x7 = (x2 ) 2 8 x 2 25x3 =4(x2 ) (2x7 ) 8 x 2 25x3 =4(2 x 2 7x4x+14 ) 8 x 2 25x3 =4(2 x 2 11x+14 ) 8 x 2 25x3 = 8 x 2 44x+56 44x25x =56+3 19x =59 x = 59 19 3 2 19
  24. 1 x1 2 x2 = 3 2x2 2 1 3 2x4 x22(x1 ) (x1 ) (x2 ) = 3 2(x1 ) 7 3 2(x2 ) x 2 2x+ 2 (x1 ) (x2 ) = 3 2(x1 ) 7 6(x2 ) x (x1 ) (x2 ) = 9(x2 ) 7(x1 ) 6 (x1 ) (x2 ) 6x =9x187x+7 6x =2x11 6x2x =11 8x =11 x = 11 8 1 3 8
  25. 1 x+3 2 5x20 = 1 1 2 3x12 2 x+3 1 x+3 2 5(x4 ) = 3 2 3 (x4 ) 2 x+3 5(x4 ) 2(x+3 ) 5(x+3 ) (x4 ) = 1 2(x4 ) 2 x+3 5x202x6 5 (x4 ) (x+3 ) = x+34(x4 ) 2 (x4 ) (x+3 ) 3x26 5 = x+34x+16 2 2(3x26 ) =5(3x+19 ) 6x52 =15x+95 6x+15x =95+52 21x =147 x = 21 x =7
  26. 1 62x 4 55x = 10 124x 3 1010x 1 2(3x ) 4 5(1x ) = (3x ) 3 10(1x ) 1 2(3x ) 4 5(1x ) = 5 2(3x ) 3 10(1x ) 5(1x ) 8(3x ) 10(3x ) (1x ) = 25(1x ) 3(3x ) 10(3x ) (1x ) 5(1x ) 8(3x ) =25(1x ) 3(3x ) 5(1x ) 25(1x ) =8(3x ) 3(3x ) (1x ) (525 ) =(3x ) (83 ) 20(1x ) =5(3x ) 20+20x =155x 20x+5x =15+20 25x =35 x = x = 7 5 1 2 5
  27. 2 3 6 x 2 9 x 2 1 = 2 3x1 2 3 6 x 2 (3x1 ) (3x+1 ) = 2 3x1 2(3x1 ) (3x+1 ) 18 x 2 3(3x+1 )(3x1 ) = 2 3x1 2(9 x 2 1 ) 18 x 2 3(3x+1 ) =2 18 x 2 2 18 x 2 =6(3x+1 ) 2 =18x+6 62 =18x 8 =18x x = x = 4 9
  28. 5 x 2 27x 5x+3 1 x =x6 x(5 x 2 27x ) (5x+3 ) x(5x+3 ) =x6 5 x 3 27 x 2 5x3 =x(5x+3 ) (x6 ) 5 x 3 27 x 2 5x3 =x(5 x 2 30x+3x18 ) 5 x 3 27 x 2 5x3 = 5 x 3 27 x 2 18x 18x5x =3 13x =3 x = 3 13
  29. 4x+1 4x1 6 16 x 2 1 = 4x1 4x+1 4x+1 4x1 6 (4x1 ) (4x+1 ) = 4x1 4x+1 (4x+1 ) 2 6 (4x+1 )(4x1 ) = 4x1 4x+1 16 x 2 +8x+16 = (4x1 ) 2 16 x 2 +8x5 = 16 x 2 8x+1 8x+8x =1+5 16x =6 x = x = 3 8
  30. 3( x1 x+1 ) +2( x+1 x4 ) = 5x(x1 ) x 2 3x4 3(x1 ) (x4 ) +2 (x+1 ) 2 (x+1 ) (x4 ) = 5x(x1 ) (x+1 ) (x4 ) 3( x 2 5x+4 ) +2( x 2 +2x+1 ) =5 x 2 5x 3 x 2 15x+12+2 x 2 +4x+2 =5 x 2 5x 5 x 2 11x+14 = 5 x 2 5x 11x+5x =14 6x =14 x = x = 7 3 2 1 3
  31. 2( x+2 x2 ) 3( x2 2x+3 ) = x 2 +78 2 x 2 x6 2(x+2 ) (2x+3 ) 3 (x2 ) 2 (x2 ) (2x+3 ) = x 2 +78 2 x 2 4x+3x6 2(2 x 2 +3x+4x+6 ) 3( x 2 4x+4 ) (x2 ) (2x+3 ) = x 2 +78 2x(x2 ) +3(x2 ) 4 x 2 +14x+ 12 3 x 2 +12x 12 (x2 ) (2x+3 ) = x 2 +78 (x2 ) (2x+3 ) x 2 +26x = x 2 +78 x = 26 x =3
  32. 1 x 2 +3x28 1 x 2 +12x+35 = 3 x 2 +x20 1 (x+7 ) (x4 ) 1 (x+7 ) (x+5 ) = 3 (x+5 ) (x4 ) x +5 x +4 (x+7 ) (x+5 ) (x4 ) = 3 (x+5 ) (x4 ) 9 =3(x+7 ) 9 =3x+21 921 =3x 12 =3x x = 3 x =4
  33. x2 x 2 +8x+7 = 2x5 x 2 49 x2 x 2 6x7 x2 (x+7 ) (x+1 ) = 2x5 (x+7 ) (x7 ) x2 (x7 ) (x+1 ) x2 (x+7 ) (x+1 ) = (2x5 ) (x+1 ) (x2 ) (x+7 ) (x7 ) (x+7 ) (x+1 ) (x2 ) (x7 ) =2 x 2 +2x5x5( x 2 +5x14 ) x 2 9x+ 14 =2 x 2 3x5 x 2 5x+ 14 x 2 9x = x 2 8x5 9x+8x =5 x =5 x =5
  34. 4x+5 15 x 2 +7x2 2x+3 12 x 2 7x10 2x5 20 x 2 29x+5 =0 4x+5 15 x 2 3x+10x2 2x+3 12 x 2 15x+8x10 2x5 20 x 2 4x25x+5 =0 4x+5 3x(5x1 ) +2(5x1 ) 2x+3 3x(4x5 ) +2(4x5 ) 2x5 4x(5x1 ) 5(5x1 ) =0 4x+5 (3x+2 ) (5x1 ) 2x+3 (3x+2 ) (4x5 ) 2x5 (4x5 ) (5x1 ) =0 (4x+5 ) (4x5 ) (2x+3 ) (5x1 ) (2x5 ) (3x+2 ) (3x+2 ) (5x1 ) (4x5 ) =0 16 x 2 25(10 x 2 2x+15x3 ) (6 x 2 +4x15x10 ) =0 16 x 2 25(10 x 2 +13x3 ) (6 x 2 11x10 ) =0 16 x 2 25 10 x 2 13x+3 6 x 2 +11x+10 =0 2x12 =0 2x =12 x = 2 x =6
  35. 7 2x+1 3 x+4 = 2 x+1 3(x+1 ) 2 x 2 +9x+4 7(x+4 ) 3(2x+1 ) (2x+1 ) (x+4 ) = 2 x+1 3(x+1 ) 2 x 2 +x+8x+4 7x+286x3 (2x+1 ) (x+4 ) = 2 x+1 3(x+1 ) x(2x+1 ) +4(2x+1 ) x+25 (2x+1 ) (x+4 ) = 2 x+1 3 (x+1 ) 2 (2x+1 ) (x+4 ) x+25 (2x+1 ) (x+4 ) = 2(2x+1 ) (x+4 ) 3( x 2 +2x+1 ) (x+1 ) (2x+1 ) (x+4 ) (x+25 ) (x+1 ) =2(2 x 2 +8x+x+4 ) 3 x 2 6x3 x 2 +26x+25 =4 x 2 +18x+83 x 2 6x3 x 2 +26x+25 = x 2 +12x+5 26x12x =25+5 14x =20 x = x = 10 7 1 3 7
  36. (x+3 ) 2 (x3 ) 2 = x1 x+1 + 2(7x+1 ) x 2 2x3 (x+3 ) 2 (x3 ) 2 = x1 x+1 + 2(7x+1 ) (x3 ) (x+1 ) (x+3 ) 2 (x3 ) 2 = (x1 ) (x3 ) +2(7x+1 ) (x3 )(x+1 ) x 2 +6x+9 x3 = x 2 4x+3+14x+2 x+1 x 2 +6x+9 x3 = x 2 +10x+5 x+1 ( x 2 +6x+9 ) (x+1 ) =(x3 ) ( x 2 +10x+5 ) x 3 +6 x 2 +9x+ x 2 +6x+9 = x 3 +10 x 2 +5x3 x 2 30x15 7 x 2 +15x+9 = 7 x 2 25x15 15x+25x =159 40x =24 x = x = 3 5
  37. x4 x+5 x+1 x2 = 12(x+3 ) (x+5 ) 2 (x4 ) (x2 ) (x+1 ) (x+5 ) (x+5 )(x2 ) = 12(x+3 ) (x+5 ) 2 x 2 6x+8( x 2 +6x+5 ) x2 = 12(x+3 ) x+5 x 2 6x+8 x 2 6x5 x2 = 12(x+3 ) x+5 12x+3 x2 = 12(x+3 ) x+5 (12x+3 ) (x+5 ) =(12x36 ) (x2 ) 12 x 2 60x+3x+15 = 12 x 2 +24x36x+72 57x =12x+7215 57x+12x =57 45x =57 x = x = 19 15 1 4 15
  38. x3 x4 x2 x3 = x+2 x+1 x+3 x+2 (x3 ) 2 (x2 ) (x4 ) (x4 ) (x3 ) = (x+2 ) 2 (x+3 ) (x+1 ) (x+1 ) (x+2 ) x 2 6x+9( x 2 6x+8 ) (x4 ) (x3 ) = x 2 +4x+4( x 2 +4x+3 ) (x+1 ) (x+2 ) x 2 6x +9 x 2 + 6x 8 (x4 ) (x3 ) = x 2 + 4x +4 x 2 4x 3 (x+1 ) (x+2 ) 1 x 2 7x+12 = 1 x 2 +3x+2 x 2 +3x+2 = x 2 7x+12 3x+7x =122 10x =10 x = 10 10 x =1
  39. x+6 x+2 x+1 x3 = x5 x1 x x+4 (x+6 ) (x3 ) (x+1 ) (x+2 ) (x+2 ) (x3 ) = (x5 ) (x+4 ) x(x1 ) (x1 ) (x+4 ) x 2 +3x18( x 2 +3x+2 ) (x+2 ) (x3 ) = x 2 x20( x 2 x ) (x1 ) (x+4 ) x 2 + 3x 18 x 2 3x 2 x 2 x6 = x 2 x 20 x 2 + x x 2 +3x4 20 x 2 x6 = 20 x 2 +3x4 1 x 2 x6 = 1 x 2 +3x4 x 2 +3x4 = x 2 x6 3x+x =6+4 4x =2 x = 2 x = 1 2

Ejercicio 141

CAPITULO XV

Ecuaciones fraccionarias de primer grado
Resolución de ecuaciones fraccionarias con denominadores monomios
Ejercicio 141
Resolver las siguientes ecuaciones:
  1. x 6 +5 = 1 3 x El m.c.m es 6, multiplicamos la ecuación por 6 x+30 =26x x+6x =230 7x =28 x = 7 x =4
  2. 3x 5 2x 3 + 1 5 =0 El m.c.m es 15, multiplicamos la ecuación por 15 9x10x+3 =0 x =3 x =3
  3. 1 2x + 1 4 1 10x = 1 5 El m.c.m es  20x , multiplicamos la ecuación por  20x 10+5x2 =4x 5x4x =8 x =8
  4. x 2 +2 x 12 = x 6 5 4 El m.c.m es 12, multiplicamos la ecuación por 12 6x+24x =2x15 5x2x =1524 3x =39 x = 3 x =13
  5. 3x 4 1 5 +2x = 5 4 3x 20 El m.c.m es 20, multiplicamos la ecuación por 20 15x4+40x =253x 55x+3x =25+4 58x =29 x = 29 x = 1 2
  6. 2 3x 5 x = 7 10 3 2x +1 El m.c.m es  30x , multiplicamos la ecuación por  30x 20150 =21x45+30x 130+45 =51x 85 =51x x = x = 5 3
  7. x4 3 5 =0 El m.c.m es , multiplicamos la ecuación por 3 x415 =0 x19 =0 x =19
  8. x x+2 12 = 5x 2 El m.c.m es 12, multiplicamos la ecuación por 12 12x(x+2 ) =30x 12xx230x =0 19x =2 x = 2 19
  9. x 5x1 3 =4x 3 5 El m.c.m es 15, multiplicamos la ecuación por 15 15x5(5x1 ) =60x9 15x25x+560x =9 70x =59 70x =14 x = 14 x = 1 5
  10. 10x 8x3 4 =2(x3 ) El m.c.m es 4, multiplicamos la ecuación por 4 40x(8x3 ) =8(x3 ) 40x8x+3 =8x24 32x8x =243 24x =27 x = x = 9 8
  11. x2 3 x3 4 = x4 5 El m.c.m es 60, multiplicamos la ecuación por 60 20(x2 ) 15(x3 ) =12(x4 ) 20x4015x+45 =12x48 5x12x+5 =48 7x =485 7x =53 x = 53 7
  12. x1 2 x2 3 x3 4 = x5 5 El m.c.m es 60, multiplicamos la ecuación por 60 30(x1 ) 20(x2 ) 15(x3 ) =12(x5 ) 30x3020x+4015x+45 =12x+60 5x+55 =12x+60 5x+12x =6055 7x =5 x = 5 7
  13. x(5x1 ) 75x 10 =1 El m.c.m es 10, multiplicamos la ecuación por 10 10x10(5x1 ) (75x ) =10 10x50x+107+5x =10 35x+3 =10 35x =7 x = 7 x = 1 5
  14. 2x 5x6 4 + 1 3 (x5 ) =5x El m.c.m es 12, multiplicamos la ecuación por 12 24x3(5x6 ) +4(x5 ) =60x 24x15x+18+4x20+60x =0 73x2 =0 73x =2 x = 2 73
  15. 4 10x+1 6 =4x 16x+3 4 El m.c.m es 12, multiplicamos la ecuación por 12 482(10x+1 ) =48x3(16x+3 ) 4820x2 = 48x 48x 9 20x =946 20x =55 x = x = 11 4
  16. 1 2 (x1 ) (x3 ) = 1 3 (x+3 ) + 1 6 El m.c.m es 6, multiplicamos la ecuación por 6 3(x1 ) 6(x3 ) =2(x+3 ) +1 3x36x+18 =2x+6+1 3x2x+15 =7 5x =15+7 5x =8 x = 8 5 1 3 5
  17. 6x+1 3 11x2 9 1 4 (5x2 ) = 5 6 (6x+1 ) El m.c.m es 36, multiplicamos la ecuación por 36 12(6x+1 ) 4(11x2 ) 9(5x2 ) =30(6x+1 ) 72x+1244x+845x+18 =180x+30 17x+38180x =30 197x =3038 197x =8 x = 8 197
  18. 4x+1 3 = 1 3 (4x1 ) 13+2x 6 1 2 (x3 ) El m.c.m es , multiplicamos la ecuación por 6 2(4x+1 ) =2(4x1 ) 132x3(x3 ) 8x+2 =8x2132x3x+9 8x =3x62 8x3x =8 5x =8 x = 8 5
  19. 2 5 (5x1 ) + 3 10 (10x3 ) = 1 2 (x2 ) 6 5 El m.c.m es 10, multiplicamos la ecuación por 10 4(5x1 ) +3(10x3 ) =5(x2 ) 12 20x4+30x9 =5x+1012 50x13 =5x2 50x+5x =132 55x =11 x = 11 x = 1 5
  20. 3x1 2 5x+4 3 x+2 8 = 2x3 5 1 10 El m.c.m es 120, multiplicamos la ecuación por 120 60(3x1 ) 40(5x+4 ) 15(x+2 ) =24(2x3 ) 12 180x60200x16015x30 =48x7212 35x25048x =84 83x =25084 83x =166 x = 83 x =2
  21. 7x1 3 52x 2x = 4x3 4 + 1+4 x 2 3x El m.c.m es  12x , multiplicamos la ecuación por  12x 4x(7x1 ) 6(52x ) =3x(4x3 ) +4(1+4 x 2 ) 28 x 2 4x30+12x =12 x 2 9x+4+16 x 2 28 x 2 +8x = 28 x 2 9x+4+30 8x+9x =34 17x =34 x = 17 x =2
  22. 2x+7 3 2( x 2 4 ) 5x 4 x 2 6 15x = 7 x 2 +6 3 x 2 El m.c.m es  15 x 2 , multiplicamos la ecuación por  15 x 2 5 x 2 (2x+7 ) 6x( x 2 4 ) x(4 x 2 6 ) =5(7 x 2 +6 ) 10 x 3 + 35 x 2 6 x 3 +24x 4 x 3 +6x = 35 x 2 +30 30x =30 x = 30 30 x =1
  23. 2 3 ( x+1 5 ) = 3 4 ( x6 3 ) El m.c.m es 60, multiplicamos la ecuación por 60 8(x+1 ) =15(x6 ) 8x+8 =15x90 8x15x =890 7x =98 x = 7 x =14
  24. 3 5 ( 2x1 6 ) 4 3 ( 3x+2 4 ) 1 5 ( x2 3 ) + 1 5 =0 El m.c.m es 60, multiplicamos la ecuación por 60 6(2x1 ) 20(3x+2 ) 4(x2 ) +12 =0 12x660x404x+8+12 =0 52x26 =0 52x =26 x = 26 x = 1 2
  25. 10 3x+5 6 =3 11 12 x 2 4 603x5 6 = 47 12 x 8 El m.c.m es 24, multiplicamos la ecuación por 24 4(553x ) =2( 47 ) 3x 22012x =943x 12x+3x =94220 9x =126 x = 9 x =14
  26. 9x27x( 1 x 1 2 ) = 1+ x 2 2 +2 3 4 9x27 x ( 2x 2 x ) = 2+x 2 2 + 11 4 9x27( 2x 2 ) = 2+x 4 + 11 4 El m.c.m es 4, multiplicamos la ecuación por 4 36x814(2x ) =2+x+11 36x828+14x =x+13 50x36x =13 49x =13+36 49x =49 x = 49 49 x =1
  27. 3x 8 7 10 12x5 16 2x3 20 + 4x+9 4 + 7 80 =0 El m.c.m es 80, multiplicamos la ecuación por 80 30x565(12x5 ) 4(2x3 ) +20(4x+9 ) +7 =0 30x4960x+258x+12+80x+180 =0 42x+168 =0 42x =168 x = 42 x =4
  28. 5x 4 3 17 (x20 ) (2x1 ) = x+24 34 El m.c.m es 68, multiplicamos la ecuación por 68 85x12(x20 ) 68(2x1 ) =2(x+24 ) 85x12x+240136x+68 =2x+48 63x+3082x =48 65x =48308 65x =260 x = 65 x =4
  29. 5+ x 4 = 1 3 (2 x 2 ) 2 3 + 1 4 (10 5x 3 ) El m.c.m es 12, multiplicamos la ecuación por 12 60+3x =( 4x 2 ) 8+ 3 ( 305x 3 ) 60+3x =2(4x ) 8+305x 60+3x = 8 2x 8 +305x 3x+7x =3060 10x =30 x = 3 0 1 0 x =3
  30. 5(x+2 ) 12 + 4 9 22x 36 =3x20 8x 12 203x 18 El m.c.m es 36, multiplicamos la ecuación por 36 15(x+2 ) +16(22x ) =108x7203(8x ) 2(203x ) 15x+30+1622+x =108x72024+3x40+6x 16x+24 =117x784 16x117x =78424 101x =808 x = 101 x =8
  31. (3 x 2 ) (1 x 3 ) =7(x x 2 ) El m.c.m es 6, multiplicamos la ecuación por 6 ( 6x 2 ) ( 3x 3 ) =42( 2xx 2 ) 3(6x ) 2(3x ) =423(2xx ) 183x6+2x =426x+3x 12x =423x x+3x =4212 2x =30 x = 2 x =15
  32. (x+3 ) (x3 ) x 2 5 4 =(x x 5 ) (3x 3 4 ) El m.c.m es 20, multiplicamos la ecuación por 20 20( x 2 9 ) 20 x 2 25 =( 5xx 5 ) ( 12x3 4 ) 20 x 2 180 20 x 2 25 =4(4x ) 5(12x3 ) 205 =16x60x+15 20515 =44x 44 =x x =5
  33. 2x(2x 3x1 8 ) = 2 3 ( x+2 6 ) 1 4 2x( 16x3x+1 8 ) = 2 3 ( x+2 ) 1 4 2x( 13x+1 8 ) = x+2 9 1 4 El m.c.m es 72, multiplicamos la ecuación por 72 144x9(13x+1 ) =8(x+2 ) 18 144x117x9 =8x+1618 27x8x =92 19x =7 x = 7 19