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CAPITULO XIV

Operaciones con Fracciones
Ejercicio 134
Simplificar:
  1. x 2 3 y 2 ÷ 2x y 3 = x 2 3 y 2 2 x y 3 = xy 6
  2. 3 a 2 b 5 x 2 ÷ a 2 b 3 = 3 a 2 b 5 x 2 a 2 b = 3 5 b 2 x 2
  3. 5 m 2 7 n 3 ÷ 10 m 4 14a n 4 = 5 m 2 7 n 3 m a n 4 = an m 2
  4. 6 a 2 x 3 ÷ a 2 x 5 = 6 a 2 x a 2 x 5 =30 x 2
  5. 15 m 2 19a x 3 ÷ 20 y 2 38 a 3 x 4 = m 2 19 a x 3 y 2 a x 4 = 3 a 2 m 2 x 2 y 2
  6. 11 x 2 y 3 7 m 2 ÷ 22 y 4 = 11 x 2 y 3 7 m 2 y 4 = x 2 14 m 2 y
  7. x1 3 ÷ 2x2 6 = x1 3 2 (x1 ) =1
  8. 3 a 2 a 2 +6ab+9 b 2 ÷ 5 a 3 a 2 b+3a b 2 = 3 a 2 a 2 +6ab+9 b 2 5 a 3 a 2 b+3a b 2 = 3( a 2 b+3a b 2 ) 5( a 2 +6ab+9 b 2 ) = 3ab (a+3b ) 5 (a+3b ) 2 = 3ab 5(a+3b )
  9. x 3 x 2 x 2 +6x ÷ 5 x 2 5x 2x+6 = x ( x 2 1 ) 2 x (x+3 ) 5x(x1 ) 2 (x+3 ) = ( x 2 1 ) 5x(x1 ) = (x1 )(x+1 ) 5x (x1 ) = x+1 5x
  10. 1 a 2 a30 ÷ 2 a 2 +a42 = 1 a 2 a30 × a 2 +a42 2 = 1 (a6 )(a+5 ) × (a+7 )(a6 ) 2 = a+7 2(a+5 )
  11. 20 x 2 30x 15 x 3 +15 x 2 ÷ 4x6 x+1 = 20 x 2 30x 15 x 3 +15 x 2 × x+1 4x6 = x (2x3 ) x 2 (x+1 ) × x+1 2 (2x3 ) = 1 3x
  12. a 2 6a+5 a 2 15a+56 ÷ a 2 +2a35 a 2 5a24 = a 2 6a+5 a 2 15a+56 × a 2 5a24 a 2 +2a35 = (a5 )(a1 ) (a8 )(a7 ) × (a8 )(a+3 ) (a+7 )(a5 ) = (a+3 ) (a1 ) a 2 49
  13. 8 x 2 +26x+15 16 x 2 9 ÷ 6 x 2 +13x5 9 x 2 1 = 8 x 2 +26x+15 16 x 2 9 × 9 x 2 1 6 x 2 +13x5 = 8 x 2 +6x+20x+15 (4x3 ) (4x+3 ) × (3x1 ) (3x+1 ) 6 x 2 2x+15x5 = 2x(4x+3 ) +5(4x+3 ) (4x3 ) (4x+3 ) × (3x1 ) (3x+1 ) 2x(3x1 ) +5(3x1 ) = (2x+5 ) (4x+3 ) (4x3 )(4x+3 ) × (3x1 )(3x+1 ) (2x+5 ) (3x1 ) = 3x+1 4x3
  14. x 3 121x x 2 49 ÷ x 2 11x x+7 = x 3 121x x 2 49 × x+7 x 2 11x = x ( x 2 121 ) (x7 )(x+7 ) × x+7 x (x11 ) = (x+11 )(x11 ) x7 × 1 x11 = x+11 x7
  15. a x 2 +5 4 a 2 1 ÷ a 3 x 2 +5 a 2 2a1 = a x 2 +5 4 a 2 1 × 2a1 a 3 x 2 +5 a 2 = a x 2 +5 (2a+1 )(2a1 ) × 2a1 a 2 (a x 2 +5 ) = 1 a 2 (2a+1 )
  16. a 4 1 a 3 + a 2 ÷ a 4 +4 a 2 +3 3 a 3 +9a = a 4 1 a 3 + a 2 × 3 a 3 +9a a 4 +4 a 2 +3 = ( a 2 +1 )( a 2 1 ) a 2 (a+1 ) × 3 a ( a 2 +3 ) ( a 2 +3 ) ( a 2 +1 ) = 3 (a+1 )(a1 ) a (a+1 ) = 3(a1 ) a
  17. x 3 +125 x 2 64 ÷ x 3 5 x 2 +25x x 2 +x56 = x 3 +125 x 2 64 × x 2 +x56 x 3 5 x 2 +25x = (x+5 )( x 2 5x+25 ) (x+8 )(x+8 ) × (x+8 )(x7 ) x ( x 2 5x+25 ) = (x+5 ) (x7 ) x(x+8 )
  18. 16 x 2 24xy+9 y 2 16x12y ÷ 64 x 3 27 y 3 32 x 2 +24xy+18 y 2 = 16 x 2 24xy+9 y 2 16x12y × 32 x 2 +24xy+18 y 2 64 x 3 27 y 3 = (4x3y ) 2 4 (4x3y ) × 4 (16 x 2 +12y+9 y 2 ) (4x3y ) (16 x 2 +12y+9 y 2 ) =1
  19. a 2 6a a 3 +3 a 2 ÷ a 2 +3a54 a 2 +9a = a 2 6a a 3 +3 a 2 × a 2 +9a a 2 +3a54 = a (a6 ) a 2 (a+3 ) × a (a+9 ) a 2 6a+9a54 = a6 a+3 × a+9 a(a6 ) +9(a6 ) = a6 a+3 × a+9 (a+9 ) (a6 ) = 1 a+3
  20. 15 x 2 +7x2 25 x 3 x ÷ 6 x 2 +13x+6 25 x 2 +10x+1 = 15 x 2 +7x2 25 x 3 x × 25 x 2 +10x+1 6 x 2 +13x+6 = 15 x 2 +10x3x2 x(25 x 2 1 ) × (5x+1 ) 2 6 x 2 +9x+4x+6 = 5x(3x+2 ) (3x+2 ) x (5x+1 )(5x1 ) × (5x+1 ) 2 3x(2x+3 ) +2(2x+3 ) = (5x1 ) (3x+2 ) x (5x1 ) × 5x+1 (3x+2 )(2x+3 ) = 5x+1 x(2x+3 )
  21. x 3 1 2 x 2 2x+2 ÷ 7 x 2 +7x+7 7 x 3 +7 = x 3 1 2 x 2 2x+2 × 7 x 3 +7 7 x 2 +7x+7 = (x1 )( x 2 +x+1 ) 2( x 2 x+1 ) × 7 ( x 3 +1 ) 7 ( x 2 +x+1 ) = (x1 )( x 2 +x+1 ) 2 ( x 2 x+1 ) × (x+1 )( x 2 x+1 ) = x 2 1 2
  22. 2mx2my+nxny 3x3y ÷ 8m+4n = 2mx2my+nxny 3x3y × 1 8m+4n = 2m(xy ) +n(xy ) 3(xy ) × 1 4(2m+n ) = (2m+n ) (xy ) 3 (xy ) × 1 4 (2m+n ) = 1 12
  23. x 2 6x+9 4 x 2 1 ÷ x 2 +5x24 2 x 2 +17x+8 = x 2 6x+9 4 x 2 1 × 2 x 2 +17x+8 x 2 +5x24 = (x3 ) 2 (2x1 ) (2x+1 ) × 2 x 2 +x+16x+8 x 2 3x+8x24 = (x3 ) 2 (2x1 ) (2x+1 ) × x(2x+1 ) +8(2x+1 ) x(x3 ) +8(x3 ) = (x3 ) 2 (2x1 )(2x+1 ) × (x+8 ) (2x+1 ) (x+8 ) (x3 ) = x3 2x1
  24. 2 a 2 +7ab15 b 2 a 3 +4 a 2 b ÷ a 2 3ab40 b 2 a 2 4ab32 b 2 = 2 a 2 +7ab15 b 2 a 3 +4 a 2 b × a 2 4ab32 b 2 a 2 3ab40 b 2 = 2 a 2 +10ab3ab15 b 2 a 2 (a+4b ) × a 2 8ab+4ab32 b 2 a 2 8ab+5ab40 b 2 = 2a(a+5b ) 3b(a+5b ) a 2 (a+4b ) × a(a8b ) +4b(a8b ) a(a8b ) +5b(a8b ) = (2a3b )(a+5b ) a 2 (a+4b ) × (a+4b ) (a8b ) (a+5b ) (a8b ) = 2a3b a 2