Ejercicio 139

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CAPITULO XIV

Operaciones con Fracciones
Ejercicio 139
Hallar el verdadero valor de:
  1. x2 x+3 parax =2 x2 x+3 = 22 2+3 = 0 5 =0
  2. x2 x3 parax =3 x2 x3 = 32 33 = 1 0 =
  3. x 2 a 2 x 2 + a 2 parax =a x 2 a 2 x 2 + a 2 = a 2 a 2 a 2 + a 2 = 0 2 a 2
  4. x 2 + y 2 x 2 y 2 parax =y x 2 + y 2 x 2 y 2 = y 2 + y 2 y 2 y 2 = 2 y 2 0 =
  5. x1 3 x2 parax =2 x1 3 x2 = (x1 ) (x2 ) 3 = x 2 3x+2 3 = 2 2 3( 2 ) +2 3 = 4 6 + 2 3 = 0 3 =0
  6. x 2 9 x 2 +x12 parax =3 x 2 9 x 2 +x12 = (x+3 )(x3 ) (x+4 )(x3 ) = x+3 x+4 = 3+3 3+4 = 6 7
  7. a 2 a6 a 2 +2a15 paraa =3 a 2 a6 a 2 +2a15 = (a3 )(a+2 ) (a+5 )(a3 ) = a+2 a+5 = 3+2 3+5 = 5 8
  8. x 2 7x+10 x 3 2 x 2 x+2 parax =2 x 2 7x+10 x 3 2 x 2 x+2 = (x5 ) (x2 ) x 2 (x2 ) (x2 ) = (x5 )(x2 ) ( x 2 1 )(x2 ) = x5 x 2 1 = 25 2 2 1 = 3 3 =1
  9. x 2 2x+1 x 3 2 x 2 x+2 parax =1 x 2 2x+1 x 3 2 x 2 x+2 = (x1 ) 2 x 2 (x2 ) (x2 ) = (x1 ) 2 ( x 2 1 ) (x2 ) = (x1 ) 2 (x+1 )(x1 )(x2 ) = x1 (x+1 ) (x2 ) = 1 1 (1+1 ) (12 ) = 0 2(1 ) =0
  10. a 3 8 a 2 +11a26 paraa =2 a 3 8 a 2 +11a26 = (a2 )( a 2 +2a+4 ) (a+13 )(a2 ) = a 2 +2a+4 a+13 = 2 2 +2( 2 ) +4 2+13 = 4+4+4 2+13 = = 4 5
  11. x 2 7x+6 x 2 2x+1 parax =1 x 2 7x+6 x 2 2x+1 = (x6 )(x1 ) (x1 ) 2 = x6 x1 = 16 11 = 5 0 =
  12. Mathematical Equation
  13. x 2 16 x 3 4 x 2 x+4 parax =4 x 2 16 x 3 4 x 2 x+4 = (x4 ) (x+4 ) x 2 (x4 ) (x4 ) = (x4 )(x+4 ) ( x 2 1 )(x4 ) = x+4 (x1 ) (x+1 ) = 4+4 (41 ) (4+1 ) = 8 3( 5 ) = 8 15
  14. 4 x 2 4x+1 4 x 2 +8x5 parax = 1 2 4 x 2 4x+1 4 x 2 +8x5 = (2x1 ) 2 4 x 2 2x+10x5 = (2x1 ) 2 2x(2x1 ) +5(2x1 ) = (2x1 ) 2 (2x+5 )(2x1 ) = 2x1 2x+5 = 2 ( 1 2 ) 1 2 ( 1 2 ) +5 = 11 1+5 =0
  15. Mathematical Equation
  16. Mathematical Equation
  17. x 3 a 3 xa parax =a x 3 a 3 xa = (xa )( x 2 +ax+ a 2 ) (xa ) = x 2 +ax+ a 2 = a 2 +a( a ) + a 2 =3 a 2
  18. a 2 2ab+ b 2 a 2 ab parab =a a 2 2ab+ b 2 a 2 ab = (ab ) 2 a (ab ) = ab a = a a a =0
  19. x 2 y 2 xy y 2 y =x x 2 y 2 xy y 2 = (xy )(x+y ) y (xy ) = x+y y = x+x x = 2 x x =2
  20. x 3 a 3 a 2 x a 3 parax =a x 3 a 3 a 2 x a 3 = (xa )( x 2 +ax+ a 2 ) a 2 (xa ) = x 2 +ax+ a 2 a 2 = a 2 +a( a ) + a 2 a 2 = 3 a 2 a 2 =3
  21. Mathematical Equation
  22. Mathematical Equation
  23. Mathematical Equation
  24. Mathematical Equation
  25. Mathematical Equation
  26. 8 x 2 +6x9 12 x 2 13x+3 parax = 3 4 8 x 2 +6x9 12 x 2 13x+3 = 8 x 2 +12x6x9 12 x 2 4x9x+3 = 4x(2x+3 ) 3(2x+3 ) 4x(3x1 ) 3(3x1 ) = (4x3 )(2x+3 ) (4x3 )(3x1 ) = 2x+3 3x1 = 2 ( 3 ) +3 3( 3 4 ) 1 = 3 2 +3 9 4 1 = 3+6 2 94 = 9 5 2 = 18 5
  27. x 3 +6 x 2 +12x+8 x 4 8 x 2 +16 parax =2 x 3 +6 x 2 +12x+8 x 4 8 x 2 +16 = ( x 3 +8 ) +(6 x 2 +12x ) ( x 2 4 ) 2 = (x+2 ) ( x 2 2x+4 ) +6x(x+2 ) [(x2 ) (x+2 ) ] 2 = (x+2 )[( x 2 2x+4 ) +6x ] (x2 ) 2 (x+2 ) 2 = x 2 +4x+4 (x2 ) 2 (x+2 ) = (x+2 ) 2 (x2 ) 2 (x+2 ) = x+2 (x2 ) 2 = 2 + 2 (22 ) 2 =0
  28. 9 x 3 +3 x 2 +3x+1 27 x 3 +1 parax = 1 3 9 x 3 +3 x 2 +3x+1 27 x 3 +1 = 3 x 2 (3x+1 ) +(3x+1 ) (3x+1 ) (9 x 2 3x+1 ) = (3 x 2 +1 )(3x+1 ) (3x+1 )(9 x 2 3x+1 ) = 3 x 2 +1 9 x 2 3x+1 = 3 ( 1 3 ) 2 +1 9 ( 1 3 ) 2 3 ( 1 3 ) +1 = 3 ( 1 3 2 ) +1 9 ( 1 3 2 ) +1+1 = 1 3 +1 3 = 1+3 3 3 = 4 9
  29. 1 x1 3 x 3 1 parax =1 1 x1 3 x 3 1 = x 2 +x+13 (x1 ) ( x 2 +x+1 ) = x 2 +x2 (x1 ) ( x 2 +x+1 ) = (x+2 )(x1 ) (x1 )( x 2 +x+1 ) = x+2 x 2 +x+1 = 1+2 1 2 +1+1 = 3 3 =1
  30. ( x 2 +3x10 ) (1+ 1 x2 ) parax =2 ( x 2 +3x10 ) (1+ 1 x2 ) =(x+5 )(x2 )( x2+1 x2 ) =(x+5 ) (x1 ) =(2+5 ) (21 ) =7( 1 ) =7