Comparte esto 👍👍
CAPITULO XIV

Operaciones con Fracciones
Ejercicio 132
Simplificar:
  1. 2 a 2 3b × 6 b 2 4a = 2 a 2 3b × 6 b 2 4 a =ab
  2. x 2 y 5 × 10 a 3 3 m 2 × 9m x 3 = x 2 y 5 × a 3 3 m 2 × m x 3 = 6 a 3 y mx
  3. 5 x 2 7 y 3 × 4 y 2 7 m 3 × 14m 5 x 4 = 5 x 2 7 y 3 × 4 y 2 7 m × m 5 x = 8 7 m 2 x 2 y
  4. 5 a × 2a b 2 × 3b 10 = 5 a × 2 a b 2 × 3 b 10 = 3 b
  5. 2 x 3 15 a 3 × 3 a 2 y × 5 x 2 7x y 2 = 2 x 3 15 a 3 × 3 a 2 y × 5 x 2 7 x y 2 = 2 x 4 7a y 3
  6. 7a 6 m 2 × 3m 10 n 2 × 5 n 4 14ax = 7 a m 2 × 3 m n 2 × 5 n a x = n 2 8mx
  7. 2 x 2 +x 6 × 8 4x+2 = x (2x+1 ) × 2 (2x+1 ) = 2x 3
  8. 5x+25 14 × 7x+7 10x+50 = 5 (x+5 ) × 7 (x+1 ) (x+5 ) = x+1 4
  9. m+n mn n 2 × n 2 m 2 n 2 = (m+n ) n (mn ) × n 2 (mn )(m+n ) = n (mn ) 2
  10. xy2 y 2 x 2 +xy × x 2 +2xy+ y 2 x 2 2xy = y (x2y ) x (x+y ) × (x+y ) 2 x (x2y ) = y(x+y ) x 2
  11. x 2 4xy+4 y 2 x 2 +2xy × x 2 x 2 4 y 2 = (x2y ) 2 x (x+2y ) × x 2 (x+2y )(x2y ) = x(x2y ) (x+2y ) 2
  12. 2 x 2 +2x 2 x 2 × x 2 3x x 2 2x3 = 2 x (x+1 ) 2 x 2 × x (x3 ) (x3 ) (x+1 ) =1
  13. a 2 ab+ab a 2 +2a+1 × 3 6 a 2 6ab = a(ab ) +(ab ) (a+1 ) 2 × 3 6a(ab ) = (ab ) (a+1 ) (a+1 ) 2 × 3 a (ab ) = 1 2(a+1 )
  14. (xy ) 3 x 3 1 × x 2 +x+1 (xy ) 2 = (xy ) 3 (x1 )( x 2 +x+1 ) × x 2 +x+1 (xy ) 2 = xy x1
  15. 2a2 2 a 2 50 × a 2 4a5 3a+3 = 2 (a1 ) 2 ( a 2 25 ) × (a5 )(a+1 ) 3 (a+1 ) = a1 (a+5 )(a5 ) × a5 3 = a1 3(a+5 )
  16. 2 x 2 3x2 6x+3 × 3x+6 x 2 4 = 2 x 2 4x+x2 3(2x+1 ) × 3 (x+2 ) (x2 )(x+2 ) = 2x(x2 ) +x2 3(2x+1 ) × 3 x2 = (2x+1 ) (x2 ) 3 (2x+1 ) × 3 (x2 ) =1
  17. y 2 +9y+18 y5 × 5y25 5y+15 = (y+6 )(y+3 ) y5 × 5 (y5 ) 5 (y+3 ) =y+6
  18. x 3 +2 x 2 3x 4 x 2 +8x+3 × 2 x 2 +3x x 2 x = x( x 2 +2x3 ) 4 x 2 +2x+6x+3 × x (2x+3 ) x (x1 ) = x(x+3 )(x1 ) 2x(2x+1 ) +3(2x+1 ) × 2x+3 x1 = x(x+3 ) (2x+3 )(2x+1 ) × (2x+3 ) = x(x+3 ) 2x+1
  19. x 3 27 a 3 1 × a 2 +a+1 x 2 +3x+9 = (x3 )( x 2 +3x+9 ) (a1 )( a 2 +a+1 ) × a 2 +a+1 x 2 +3x+9 = x3 a1
  20. a 2 +4ab+4 b 2 3 × 2a+4b (a+2b ) 3 = (a+2b ) 2 3 × 2 (a+2b ) (a+2b ) 3 = 2 3
  21. 1x a+1 × a 2 +a x x 2 × x 2 a = 1x a+1 × a (a+1 ) x (1x ) × x 2 a =x
  22. x 2 +2x x 2 16 × x 2 2x8 x 3 + x 2 × x 2 +4x x 2 +4x+4 = x (x+2 ) (x4 )(x+4 ) × x 2 4x+2x8 x 2 (x+1 ) × x (x+4 ) (x+2 ) 2 = 1 x4 × x(x4 ) +2(x4 ) x+1 × 1 x+2 = 1 x4 × (x4 ) (x+2 ) x+1 × 1 x+2 = 1 x+1
  23. (m+n ) 2 x 2 (m+x ) 2 n 2 × (mn ) 2 x 2 m 2 +mnmx = [(m+n ) x ] [(m+n ) +x ] [(m+x ) n ] [(m+x ) +n ] × [(mn ) x ] [(mn ) +x ] m(m+nx ) = [m+nx ] [m+n+x ] [m+xn ] [m+x+n ] × [mnx ][mn+x ] m (m+nx ) = mnx m
  24. 2 a 3 +2a b 2 2a x 2 2ax × x 3 x a 2 x+ b 2 x × x x+1 = 2a ( a 2 + b 2 ) 2a x (x1 ) × x ( x 2 1 ) x ( a 2 + b 2 ) × x x+1 = 1 x1 × (x1 ) (x+1 ) × 1 x+1 =1
  25. a 2 5a+6 3a15 × 6a a 2 a30 × a 2 25 2a4 = (a3 )(a2 ) 3 (a5 ) × 6 a (a6 )(a+5 ) × (a+5 ) (a5 ) 2 (a2 ) = a(a3 ) a6
  26. x 2 3xy10 y 2 x 2 2xy8 y 2 × x 2 16 y 2 x 2 +4xy × x 2 6xy x+2y = (x5y )(x+2y ) (x4y ) (x+2y ) × (x4y ) (x+4y ) x (x+4y ) × x (x6y ) x+2y = (x5y ) (x6y ) x+2y
  27. x 2 +4ax+4 a 2 3ax6 a 2 × 2ax4 a 2 ax+a × 6a+6x x 2 +3ax+2 a 2 = (x+2a ) 2 3 a (x2a ) × 2 a (x2a ) a (x+1 ) × (a+x ) (x+2a ) (x+a ) = 4(x+2a ) a(x+1 )
  28. a 2 81 2 a 2 +10a × a+11 a 2 36 × 2a12 2a+18 × a 3 +5 a 2 2a+22 = (a+9 )(a9 ) 2 a (a+5 ) × a+11 (a6 )(a+6 ) × 2 (a6 ) 2 (a+9 ) × a 2 (a+5 ) 2 (a+11 ) = a(a9 ) 4(a+6 )
  29. a 2 +7a+10 a 2 6a7 × a 2 3a4 a 2 +2a15 × a 3 2 a 2 3a a 2 2a8 = (a+5 ) (a+2 ) (a7 )(a+1 ) × (a4 ) (a+1 ) (a+5 )(a3 ) × a( a 2 2a3 ) (a4 ) (a+2 ) = 1 a7 × 1 a3 × a (a3 )(a+1 ) = a(a+1 ) a7
  30. x 4 +27x x 3 x 2 +x × x 4 +x x 4 3 x 3 +9 x 2 × 1 x (x+3 ) 2 × x 2 x3 = x ( x 3 +27 ) x ( x 2 x+1 ) × x ( x 3 +1 ) x 2 ( x 2 3x+9 ) × 1 x (x+3 ) 2 × x 2 x3 = (x+3 ) ( x 2 3x+9 ) x 2 x+1 × (x+1 )( x 2 x+1 ) x 2 3x+9 × 1 (x+3 ) 2 × 1 x3 = x+1 (x+3 ) (x3 ) = x+1 x 2 9