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CAPITULO XIII

Simplificación de fracciones
Reducir una expresión mixta a fraccionaria
Ejercicio 124
Reducir a fracción:
  1. a+ 4a a+2 = a(a+2 ) +4a a+2 = a 2 +2a+4a a+2 = a 2 +6a a+2 = a(a+6 ) a+2
  2. mn n 2 m = (mn ) m n 2 m = m 2 mn n 2 m
  3. x+5 3 x2 = x(x2 ) +5(x2 ) 3 x2 = x 2 2x+5x103 x2 = x 2 +3x13 x2
  4. a+ ab a+b = a(a+b ) +ab a+b = a[(a+b ) +b ] a+b = a[a+b+b ] a+b = a(a+2b ) a+b
  5. 1 a 2 a +a3 = 1 a 2 + a 2 3a a = 13a a
  6. 1 a+x ax = a x a x ax = 2x ax = 2x xa
  7. 2a+x a+x 1 = 2a+ x a x a+x = a a+x
  8. x+2 3 x1 = x(x1 ) +2(x1 ) 3 x1 = x 2 x+2x23 x1 = x 2 +x5 x1
  9. x 2 3x x 2 6x x+2 = ( x 2 3x ) (x+2 ) ( x 2 6x ) x+2 = x 3 3 x 2 +2 x 2 6x x 2 + 6x x+2 = x 3 2 x 2 x+2 = x 2 (x2 ) x+2
  10. x+y+ x 2 y 2 xy =x+y+ (x+y )(xy ) xy =x+y+x+y =2x+2y =2(x+y )
  11. 3mn mn +m2n = 3mn+m(mn ) 2n(mn ) mn = 3mn + m 2 mn 2mn +2 n 2 mn = m 2 +2 n 2 mn
  12. 2a3x 5ax6 x 2 a+2x =2a3x x(5a6x ) a+2x = 2a(a+2x ) 3x(a+2x ) x(5a6x ) a+2x = 2 a 2 +4ax3ax 6 x 2 5ax+ 6 x 2 a+2x = 2 a 2 4ax a+2x = 2a(a2x ) a+2x
  13. m 2 2m+4 m 3 m+2 = m 2 (m+2 ) 2m(m+2 ) +4(m+2 ) m 3 m+2 = m 3 + 2 m 2 2 m 2 4m + 4m +8 m 3 m+2 = 8 m+2
  14. x 2 5x 3x(x+2 ) x2 = x 2 (x2 ) 5x(x2 ) 3x(x+2 ) x2 = x 3 2 x 2 5 x 2 +10x3 x 2 6x x2 = x 3 10 x 2 +4x x2 = x( x 2 10x+4 ) x2
  15. a 2 +3ab b 2 + 7a b 2 b 3 2ab = ( a 2 +3ab b 2 ) (2ab ) +7a b 2 b 3 2ab = 2 a 3 +6 a 2 b2a b 2 a 2 b3a b 2 + b 3 +7a b 2 b 3 2ab = 2 a 3 +5 a 2 b+2a b 2 2ab = a(2 a 2 +5ab+2 b 2 ) 2ab
  16. x 3 +2 x 2 x+1 (x+1 ) = x 3 +2(x+1 ) ( x 2 x+1 ) x 2 x+1 = x 3 +2( x 3 +1 ) x 2 x+1 = x 3 +2 x 3 1 x 2 x+1 = 1 x 2 x+1
  17. x+3 x 3 2 x 2 +1 x 2 4x+3 = (x+3 ) ( x 2 4x+3 ) ( x 3 2 x 2 +1 ) x 2 4x+3 = x 3 4 x 2 +3x+3 x 2 12x+9 x 3 +2 x 2 1 (x3 ) (x1 ) = x 2 9x+8 (x3 ) (x1 ) = (x8 )(x1 ) (x3 )(x1 ) = x8 x3
  18. 3a+ 3 a 2 b+3a b 2 a 2 b 2 =3a+ 3ab (a+b ) (a+b )(ab ) =3a+ 3ab ab = 3a(ab ) +3ab ab = 3 a 2 3ab + 3ab ab = 3 a 2 ab
  19. x3 x 3 27 x 2 6x+9 =x3 (x3 )( x 2 +3x+9 ) (x3 ) 2 =x3 x 2 +3x+9 x3 = (x3 ) 2 ( x 2 +3x+9 ) x3 = x 2 6x+ 9 x 2 3x 9 x3 = 9x x3 = 9x 3x
  20. a 2 3a+5+ 2 a 3 11a+9 a 2 +a2 = a 2 3a+5+ 2 a 3 2a9a+9 (a+2 ) (a1 ) = a 2 3a+5+ 2a( a 2 1 ) 9(a1 ) (a+2 ) (a1 ) = a 2 3a+5+ 2a(a1 ) (a+1 ) 9(a1 ) (a+2 ) (a1 ) = a 2 3a+5+ (a1 )[2a(a+1 ) 9 ] (a+2 )(a1 ) = a 2 3a+5+ 2 a 2 +2a9 a+2 = ( a 2 3a+5 ) (a+2 ) +2 a 2 +2a9 a+2 = a 3 3 a 2 +5a+2 a 2 6a+10+2 a 2 +2a9 a+2 = a 3 + a 2 +a+1 a+2 = a 2 (a+1 ) +(a+1 ) a+2 = ( a 2 +1 ) (a+1 ) a+2