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CAPITULO XIII

Reducción de fracciones
Reducir una fracción a expresión entera o mixta
Ejercicio 123
Reducir a expresión entera o mixta:
  1. 6 a 3 10 a 2 2a
    6 a 3 10 a 2 2a = a 3 2a a 2 2a =3 a 2 5a
  2. 9 x 2 y6 x 2 y 2 +3x y 3 3xy
    9 x 2 y6 x 2 y 2 +3x y 3 3xy = x 2 y 3xy x 2 y 2 3xy + 3x y 3 3xy =3x2xy+ y 2
  3. x 2 +3 x
    x 2 +3 x = x 2 x + 3 x =x+ 3 x
  4. 10 a 2 +15a2 5a

    Mathematical Equation

    2a+3 2 5a
  5. 9 x 3 6 x 2 +3x5 3x

    Mathematical Equation

    3 x 2 2x+1 5 3x
  6. x 2 5x16 x+2

    Mathematical Equation

    x7 2 x+2
  7. 12 x 2 6x2 4x1

    Mathematical Equation

    3x 3 4 11 4 4x1 =3x 3 4 11 4(4x1 ) =3x 3(4x1 ) +11 4(4x1 ) =3x 12x3+11 4(4x1 ) =3x 12x+8 4(4x1 ) =3x 4 (3x+2 ) 4 (4x1 ) =3x 3x+2 4x1
  8. a 3 +3 b 3 a+2b

    Mathematical Equation

    a 2 2ab+4 b 2 5 b 3 a+2b
  9. x 3 x 2 6x+1 x 2 3

    Mathematical Equation

    x1 3x+2 x 2 3
  10. 3 x 3 +4 x 2 y+2x y 2 6 y 3 3x2y

    Mathematical Equation

    x 2 +2xy+2 y 2 2 y 3 3x2y
  11. 2 x 3 7 x 2 +6x8 2 x 2 x+1

    Mathematical Equation

    x3+ 2x5 2 x 2 x+1
  12. 2 a 4 3 a 3 + a 2 a 2 a+1

    Mathematical Equation

    2 a 2 a2 a2 a 2 a+1
  13. x 4 4 x 2 3x x 2 2

    Mathematical Equation

    x 2 2 3x+4 x 2 2
  14. 10 n 3 18 n 2 5n+3 2 n 2 3n+1

    Mathematical Equation

    5n 3 2 + 29 2 n+ 9 2 2 n 2 3n+1 =5n 3 2 + 929n 2 2 n 2 3n+1 =5n 3 2 + 29n+9 2(2 n 2 3n+1 ) =5n 1 2 (3 929n 2 n 2 3n+1 ) =5n 1 2 ( 6 n 2 9n+39+29n 2 n 2 3n+1 ) =5n 1 2 ( 6 n 2 +20n6 2 n 2 3n+1 ) =5n 1 2 [ 2 (3 n 2 +10n3 ) 2 n 2 3n+1 ] =5n 3 n 2 +10n3 2 n 2 3n+1
  15. 8 x 4 4 x 2 +5x+6

    Mathematical Equation

    2 x 2 5 2 x+ 1 8 + 115 8 x 3 4 4 x 2 +5x+6 =2 x 2 5 2 x+ 1 8 + 115x6 8 4 x 2 +5x+6 =2 x 2 5 2 x+ 1 8 + 115x6 8(4 x 2 +5x+6 ) =2 x 2 1 2 [5x 1 4 115x6 4(4 x 2 +5x+6 ) ] =2 x 2 1 2 [ 20x(4 x 2 +5x+6 ) (4 x 2 +5x+6 ) 115x+6 4(4 x 2 +5x+6 ) ] =2 x 2 1 2 [ 80 x 3 +100 x 2 + 120x 4 x 2 5x 6 115x + 6 4(4 x 2 +5x+6 ) ] =2 x 2 1 2 [ 80 x 3 +96 x 2 4(4 x 2 +5x+6 ) ] =2 x 2 1 2 [ 8 (10 x 3 +12 x 2 ) 4 (4 x 2 +5x+6 ) ] =2 x 2 10 x 3 +12 x 2 4 x 2 +5x+6
  16. 6 m 5 +3 m 4 n 3 m 3 m n 2 + n 3

    Mathematical Equation

    2 m 2 +mn+ 2 3 n 2 + m 2 n 3 1 3 m n 4 2 3 n 5 3 m 3 m n 2 + n 3 =2 m 2 +mn+ 2 3 n 2 + 3 m 2 n 3 m n 4 2 n 5 3 3 m 3 m n 2 + n 3 =2 m 2 +mn+ 2 3 n 2 + 3 m 2 n 3 m n 4 2 n 5 3(3 m 3 m n 2 + n 3 ) =2 m 2 +mn+ 1 3 [2 n 2 + 3 m 2 n 3 m n 4 2 n 5 3 m 3 m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 2 n 2 (3 m 3 m n 2 + n 3 ) 3 m 2 n 3 m n 4 2 n 5 3 m 3 m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 6 m 3 n 2 2m n 4 + 2 n 5 3 m 2 n 3 m n 4 2 n 5 3 m 3 m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 6 m 3 n 2 3 m 2 n 3 3m n 4 3 m 3 m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 3 (2 m 3 n 2 m 2 n 3 m n 4 ) 3 m 3 m n 2 + n 3 ] =2 m 2 +mn+ 2 m 3 n 2 m 2 n 3 m n 4 3 m 3 m n 2 + n 3