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Ejercicio 134

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CAPITULO XIV

Operaciones con Fracciones
Ejercicio 134
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  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. x–1 3 ÷ 2x–2 6 = x–1 3 2 ( x–1 ) =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( x–1 ) 2 ( x+3 ) = ( x 2 –1 ) 5x( x–1 ) = ( x–1 ) ( x+1 ) 5x ( x–1 ) = x+1 5x
  10. 1 a 2 –a–30 ÷ 2 a 2 +a–42 = 1 a 2 –a–30 × a 2 +a–42 2 = 1 ( a–6 ) ( a+5 ) × ( a+7 ) ( a–6 ) 2 = a+7 2( a+5 )
  11. 20 x 2 –30x 15 x 3 +15 x 2 ÷ 4x–6 x+1 = 20 x 2 –30x 15 x 3 +15 x 2 × x+1 4x–6 = x ( 2x–3 ) x 2 ( x+1 ) × x+1 2 ( 2x–3 ) = 1 3x
  12. a 2 –6a+5 a 2 –15a+56 ÷ a 2 +2a–35 a 2 –5a–24 = a 2 –6a+5 a 2 –15a+56 × a 2 –5a–24 a 2 +2a–35 = ( a–5 ) ( a–1 ) ( a–8 ) ( a–7 ) × ( a–8 ) ( a+3 ) ( a+7 ) ( a–5 ) = ( a+3 ) ( a–1 ) a 2 –49
  13. 8 x 2 +26x+15 16 x 2 –9 ÷ 6 x 2 +13x–5 9 x 2 –1 = 8 x 2 +26x+15 16 x 2 –9 × 9 x 2 –1 6 x 2 +13x–5 = 8 x 2 +6x+20x+15 ( 4x–3 ) ( 4x+3 ) × ( 3x–1 ) ( 3x+1 ) 6 x 2 –2x+15x–5 = 2x( 4x+3 ) +5( 4x+3 ) ( 4x–3 ) ( 4x+3 ) × ( 3x–1 ) ( 3x+1 ) 2x( 3x–1 ) +5( 3x–1 ) = ( 2x+5 ) ( 4x+3 ) ( 4x–3 ) ( 4x+3 ) × ( 3x–1 ) ( 3x+1 ) ( 2x+5 ) ( 3x–1 ) = 3x+1 4x–3
  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 ) ( x–7 ) ( x+7 ) × x+7 x ( x–11 ) = ( x+11 ) ( x–11 ) x–7 × 1 x–11 = x+11 x–7
  15. a x 2 +5 4 a 2 –1 ÷ a 3 x 2 +5 a 2 2a–1 = a x 2 +5 4 a 2 –1 × 2a–1 a 3 x 2 +5 a 2 = a x 2 +5 ( 2a+1 ) ( 2a–1 ) × 2a–1 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 ) ( a–1 ) a ( a+1 ) = 3( a–1 ) a
  17. x 3 +125 x 2 –64 ÷ x 3 –5 x 2 +25x x 2 +x–56 = x 3 +125 x 2 –64 × x 2 +x–56 x 3 –5 x 2 +25x = ( x+5 ) ( x 2 –5x+25 ) ( x+8 ) ( x+8 ) × ( x+8 ) ( x–7 ) x ( x 2 –5x+25 ) = ( x+5 ) ( x–7 ) x( x+8 )
  18. 16 x 2 –24xy+9 y 2 16x–12y ÷ 64 x 3 –27 y 3 32 x 2 +24xy+18 y 2 = 16 x 2 –24xy+9 y 2 16x–12y × 32 x 2 +24xy+18 y 2 64 x 3 –27 y 3 = ( 4x–3y ) 2 4 ( 4x–3y ) × 4 ( 16 x 2 +12y+9 y 2 ) ( 4x–3y ) ( 16 x 2 +12y+9 y 2 ) =1
  19. a 2 –6a a 3 +3 a 2 ÷ a 2 +3a–54 a 2 +9a = a 2 –6a a 3 +3 a 2 × a 2 +9a a 2 +3a–54 = a ( a–6 ) a 2 ( a+3 ) × a ( a+9 ) a 2 –6a+9a–54 = a–6 a+3 × a+9 a( a–6 ) +9( a–6 ) = a–6 a+3 × a+9 ( a+9 ) ( a–6 ) = 1 a+3
  20. 15 x 2 +7x–2 25 x 3 –x ÷ 6 x 2 +13x+6 25 x 2 +10x+1 = 15 x 2 +7x–2 25 x 3 –x × 25 x 2 +10x+1 6 x 2 +13x+6 = 15 x 2 +10x–3x–2 x( 25 x 2 –1 ) × ( 5x+1 ) 2 6 x 2 +9x+4x+6 = 5x( 3x+2 ) –( 3x+2 ) x ( 5x+1 ) ( 5x–1 ) × ( 5x+1 ) 2 3x( 2x+3 ) +2( 2x+3 ) = ( 5x–1 ) ( 3x+2 ) x ( 5x–1 ) × 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 = ( x–1 ) ( x 2 +x+1 ) 2( x 2 –x+1 ) × 7 ( x 3 +1 ) 7 ( x 2 +x+1 ) = ( x–1 ) ( x 2 +x+1 ) 2 ( x 2 –x+1 ) × ( x+1 ) ( x 2 –x+1 ) = x 2 –1 2
  22. 2mx–2my+nx–ny 3x–3y ÷ 8m+4n = 2mx–2my+nx–ny 3x–3y × 1 8m+4n = 2m( x–y ) +n( x–y ) 3( x–y ) × 1 4( 2m+n ) = ( 2m+n ) ( x–y ) 3 ( x–y ) × 1 4 ( 2m+n ) = 1 12
  23. x 2 –6x+9 4 x 2 –1 ÷ x 2 +5x–24 2 x 2 +17x+8 = x 2 –6x+9 4 x 2 –1 × 2 x 2 +17x+8 x 2 +5x–24 = ( x–3 ) 2 ( 2x–1 ) ( 2x+1 ) × 2 x 2 +x+16x+8 x 2 –3x+8x–24 = ( x–3 ) 2 ( 2x–1 ) ( 2x+1 ) × x( 2x+1 ) +8( 2x+1 ) x( x–3 ) +8( x–3 ) = ( x–3 ) 2 ( 2x–1 ) ( 2x+1 ) × ( x+8 ) ( 2x+1 ) ( x+8 ) ( x–3 ) = x–3 2x–1
  24. 2 a 2 +7ab–15 b 2 a 3 +4 a 2 b ÷ a 2 –3ab–40 b 2 a 2 –4ab–32 b 2 = 2 a 2 +7ab–15 b 2 a 3 +4 a 2 b × a 2 –4ab–32 b 2 a 2 –3ab–40 b 2 = 2 a 2 +10ab–3ab–15 b 2 a 2 ( a+4b ) × a 2 –8ab+4ab–32 b 2 a 2 –8ab+5ab–40 b 2 = 2a( a+5b ) –3b( a+5b ) a 2 ( a+4b ) × a( a–8b ) +4b( a–8b ) a( a–8b ) +5b( a–8b ) = ( 2a–3b ) ( a+5b ) a 2 ( a+4b ) × ( a+4b ) ( a–8b ) ( a+5b ) ( a–8b ) = 2a–3b a 2
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