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Ejercicio 120

Gestor Baldor
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DESCARGA
CAPITULO XIII

Simplificación de fracciones
Simplificación de fracciones cuyos términos sean polinomios. Caso en que hay que cambiar el signo a uno o más factores
Ejercicio 120
Simplificar o reducir a su más simple expresión:
  1. 4–4x 6x–6 =– 4x–4 6x–6 =– ( x–1 ) ( x–1 ) =– 2 3
  2. a 2 – b 2 b 2 – a 2 =– a 2 – b 2 a 2 – b 2 =–1
  3. m 2 – n 2 ( n–m ) 2 =– n 2 – m 2 ( n–m ) 2 =– ( n–m ) ( n+m ) ( n–m ) 2 =– n+m n–m
  4. x 2 –x–12 16– x 2 =– x 2 –x–12 x 2 –16 =– ( x–4 ) ( x+3 ) ( x–4 ) ( x+4 ) =– x+3 x+4
  5. 3y–6x 2mx–my–2nx+ny = 3( y–2x ) 2mx–2nx–my+ny = 3( y–2x ) 2x( m–n ) –y( m–n ) = 3( y–2x ) ( m–n ) ( 2x–y ) = 3 ( y–2x ) ( n–m ) ( y–2x ) = 3 n–m
  6. 2 x 2 –9x–5 10+3x– x 2 =– 2 x 2 +x–10x–5 x 2 –3x–10 =– x( 2x+1 ) –5( 2x+1 ) ( x–5 ) ( x+2 ) =– ( 2x+1 ) ( x–5 ) ( x–5 ) ( x+2 ) =– 2x+1 x+2
  7. 8– a 3 a 2 +2a–8 =– a 3 –8 a 2 +2a–8 =– ( a–2 ) ( a 2 +2a+4 ) ( a+4 ) ( a–2 ) =– a 2 +2a+4 a+4
  8. a 2 +a–2 n–an–m+am = ( a+2 ) ( a–1 ) n–m–( an–am ) = ( a+2 ) ( a–1 ) n–m–a( n–m ) = ( a+2 ) ( a–1 ) ( 1–a ) ( n–m ) = ( a+2 ) ( a–1 ) ( a–1 ) ( m–n ) = a+2 m–n
  9. 4 x 2 –4xy+ y 2 5y–10x = ( 2x–y ) 2 5( y–2x ) =– ( 2x–y ) 2 5 ( 2x–y ) =– 2x–y 5
  10. 3mx–nx–3my+ny n y 2 –n x 2 –3m y 2 +3m x 2 = 3mx–3my–( nx–ny ) ( n y 2 –n x 2 ) –( 3m y 2 –3m x 2 ) = 3m( x–y ) –n( x–y ) n( y 2 – x 2 ) –3m( y 2 – x 2 ) = ( 3m–n ) ( x–y ) ( y 2 – x 2 ) ( n–3m ) = ( 3m–n ) ( x–y ) ( x 2 – y 2 ) ( 3m–n ) = x–y ( x–y ) ( x+y ) = 1 x+y
  11. 9–6x+ x 2 x 2 –7x+12 = ( 3–x ) 2 ( x–4 ) ( x–3 ) = ( 3–x ) 2 ( 4–x ) ( 3–x ) = 3–x 4–x
  12. a 2 – b 2 b 3 – a 3 = ( a–b ) ( a+b ) ( b–a ) ( b 2 +ab+ a 2 ) =– ( b–a ) ( a+b ) ( b–a ) ( b 2 +ab+ a 2 ) =– a+b b 2 +ab+ a 2
  13. 3ax–3bx–6a+6b 2b–2a–bx+ax = 3x( a–b ) –6( a–b ) 2( b–a ) –x( b–a ) = ( 3x–6 ) ( a–b ) ( b–a ) ( 2–x ) = 3 ( x–2 ) ( a–b ) ( a–b ) ( x–2 ) =3
  14. a 2 – x 2 x 2 –ax–3x+3a = ( a–x ) ( a+x ) x( x–a ) –3( x–a ) = ( a–x ) ( a+x ) ( x–a ) ( x–3 ) = ( a–x ) ( a+x ) ( a–x ) ( 3–x ) = a+x 3–x
  15. 3bx–6x 8– b 3 = 3x( b–2 ) ( 2–b ) ( 4+2b+ b 2 ) =– 3x ( b–2 ) ( b–2 ) ( 4+2b+ b 2 ) =– 3x 4+2b+ b 2
  16. ( 1–a ) 3 a–1 =– ( 1–a ) 1–a =– ( 1–a ) 2
  17. 2 x 3 –2 x 2 y–2x y 2 3 y 3 +3x y 2 –3 x 2 y = 2x( x 2 –xy– y 2 ) 3y( y 2 +xy– x 2 ) =– 2x ( x 2 –xy– y 2 ) 3y ( x 2 –xy– y 2 ) =– 2x 3y
  18. ( a–b ) 3 ( b–a ) 2 = ( a–b ) 3 ( a–b ) 2 =a–b
  19. 2 x 2 –22x+60 75–3 x 2 = 2( x 2 –11x+30 ) 3( 25– x 2 ) = 2( x–6 ) ( x–5 ) 3( 5–x ) ( 5+x ) = 2( 6–x ) ( 5–x ) 3 ( 5–x ) ( 5+x ) = 2( 6–x ) 3( 5+x )
  20. 6a n 2 –3 b 2 n 2 b 4 –4a b 2 +4 a 2 = 3 n 2 ( 2a– b 2 ) ( b 2 –2a ) 2 =– 3 n 2 ( b 2 –2a ) ( b 2 –2a ) 2 = 3 n 2 2a– b 2
  21. ( x–y ) 2 – z 2 ( y+z ) 2 – x 2 = [ ( x–y ) –z ] [ ( x–y ) +z ] [ ( y+z ) –x ] [ ( y+z ) +x ] = ( x–y–z ) ( x–y+z ) ( y+z–x ) ( y+z+x ) = ( y+z–x ) ( y–x–z ) ( y+z–x ) ( y+z+x ) = y–x–z y+z+x
  22. 3 a 2 –3ab bd–ad–bc+ac = 3a( a–b ) d( b–a ) –c( b–a ) = 3a( a–b ) ( d–c ) ( b–a ) = 3a ( a–b ) ( c–d ) ( a–b ) = 3a c–d
  23. ( x–5 ) 3 125– x 3 =– ( x–5 ) 3 x 3 –125 =– ( x–5 ) ( x–5 ) ( x 2 +5x+25 ) =– ( x–5 ) 2 x 2 +5x+25
  24. 13x–6–6 x 2 6 x 2 –13x+6 =– 6 x 2 –13x+6 6 x 2 –13x+6 =–1
  25. 2 x 3 –2x y 2 + x 2 – y 2 2x y 2 + y 2 –2 x 3 – x 2 = 2x( x 2 – y 2 ) +( x 2 – y 2 ) y 2 ( 2x+1 ) – x 2 ( 2x+1 ) = ( 2x+1 ) ( x 2 – y 2 ) ( y 2 – x 2 ) ( 2x+1 ) =– x 2 – y 2 x 2 – y 2 =–1
  26. 30 x 2 y–45x y 2 –20 x 3 8 x 3 +27 y 3 = 5x( 6xy–9 y 2 –4 x 2 ) ( 2x+3y ) ( 4 x 2 –6xy+9 y 2 ) =– 5x ( 4 x 2 –6xy+9 y 2 ) ( 2x+3y ) ( 4 x 2 –6xy+9 y 2 ) =– 5x 2x+3y
  27. n+1– n 3 – n 2 n 3 –n–2 n 2 +2 = n+1– n 2 ( n+1 ) n( n 2 –1 ) –2( n 2 –1 ) = ( 1– n 2 ) ( n+1 ) ( n 2 –1 ) ( n–2 ) = ( n 2 –1 ) ( n+1 ) ( n 2 –1 ) ( 2–n ) = n+1 2–n
  28. ( x–2 ) 2 ( x 2 +x–12 ) ( 2–x ) ( 3–x ) 2 = ( 2–x ) 2 ( x+4 ) ( x–3 ) ( 2–x ) ( 3–x ) 2 = ( x–2 ) ( x+4 ) ( 3–x ) ( 3–x ) 2 = ( x–2 ) ( x+4 ) 3–x
  29. 5 x 3 –15 x 2 y 90 x 3 y 2 –10 x 5 = 5 x 2 ( x–3y ) x 3 ( 9 y 2 – x 2 ) = x–3y 2x( 3y–x ) ( 3y+x ) =– x–3y 2x ( x–3y ) ( 3y+x ) =– 1 2x( 3y+x )
  30. ( x 2 –1 ) ( x 2 –8x+16 ) ( x 2 –4x ) ( 1– x 2 ) = ( x 2 –1 ) ( x 2 –8x+16 ) ( 4x– x 2 ) ( x 2 –1 ) = ( x–4 ) 2 x( 4–x ) =– ( x–4 ) 2 x ( x–4 ) =– x–4 x = 4–x x
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