Ejercicio 133

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CAPITULO XIV

Operaciones con Fracciones
Ejercicio 133
Simplificar:
  1. (a+ a b ) (a a b+1 ) =( ab+a b ) [ a(b+1 ) a b+1 ] = a (b+1 ) b ( ab+ a a b+1 ) = a 2 b b = a 2
  2. (x 2 x+1 ) (x+ 1 x+2 ) =[ x(x+1 ) 2 x+1 ] [ x(x+2 ) +1 x+2 ] =[ x 2 +x2 x+1 ] [ x 2 +2x+1 x+2 ] = (x+2 )(x1 ) x+1 (x+1 ) 2 x+2 = x 2 1
  3. (1 x a+x ) (1+ x a ) =[ a+ x x a+x ] [ a+x a ] = a a =1
  4. (a+ ab ab ) (1 b 2 a 2 ) =[ a(ab ) +ab ab ] [ a 2 b 2 a 2 ] =[ a 2 ab + ab ab ] (a+b )(ab ) a 2 = a 2 (a+b ) a 2 =a+b
  5. (x+2 12 x+1 ) (x2+ 103x x+5 ) =[ (x+1 ) (x+2 ) 12 x+1 ] [ (x2 ) (x+5 ) +103x x+5 ] =[ x 2 +3x+212 x+1 ] [ x 2 + 3x 10 + 10 3x x+5 ] =[ x 2 +3x10 x+1 ] ( x 2 x+5 ) = (x+5 )(x2 ) x+1 ( x 2 x+5 ) = x 2 (x2 ) x+1
  6. (1+ x y ) (x x 2 x+y ) =( y+x y ) [ x(x+y ) x 2 x+y ] =( 1 y ) [ x 2 +xy x 2 x+y ] = x y y =x
  7. (a+x ax+ x 2 a+2x ) (1+ x a+x ) =[ (a+x ) (a+2x ) (ax+ x 2 ) a+2x ] [ a+x+x a+x ] =[ a 2 +2ax+ ax +2 x 2 ax x 2 a+2x ] [ a+2x a+x ] =( a 2 +2ax+ x 2 ) ( 1 a+x ) = (a+x ) 2 ( 1 a+x ) =a+x
  8. (x x 3 6x x 2 25 ) (x+1 8 x+3 ) =[ x( x 2 25 ) ( x 3 6x ) x 2 25 ] [ (x+1 ) (x+3 ) 8 x+3 ] =[ x 3 25x x 3 +6x x 2 25 ] [ x 2 +4x+38 x+3 ] =( 19x x 2 25 ) ( x 2 +4x5 x+3 ) =[ 19x (x5 )(x+5 ) ] [ (x+5 )(x1 ) x+3 ] = 19x19 x 2 (x5 ) (x+3 )
  9. (m mn m+n ) (1+ n 3 m 3 ) =[ m(m+n ) mn m+n ] ( m 3 + n 3 m 3 ) =[ m 2 + mn mn m+n ] [ (m+n )( m 2 mn+ n 2 ) m 3 ] = m 2 (m+n )( m 2 mn+ n 2 ) m 3 = m 2 mn+ n 2 m
  10. (a+2x 14 x 2 2a+x ) (ax+ a 2 +5 x 2 a+4x ) =[ (a+2x ) (2a+x ) 14 x 2 2a+x ] [ (ax ) (a+4x ) + a 2 +5 x 2 a+4x ] =[ 2 a 2 +ax+4ax+2 x 2 14 x 2 2a+x ] [ a 2 +4axax4 x 2 + a 2 +5 x 2 a+4x ] =[ 2 a 2 +5ax12 x 2 2a+x ] [ 2 a 2 +3ax+ x 2 a+4x ] =[ 2 a 2 3ax+8ax12 x 2 2a+x ] [ 2 a 2 +2ax+ax+ x 2 a+4x ] =[ a(2a3x ) +4x(2a3x ) 2a+x ] [ 2a(a+x ) +x(a+x ) a+4x ] = (a+4x )(2a3x ) 2a+x × (2a+x )(a+x ) a+4x =(2a3x ) (a+x )
  11. (1+ a b ) (1 b a ) (1+ b 2 a 2 b 2 ) =( b+a b ) ( ab a ) [ a 2 b 2 + b 2 (ab ) (a+b ) ] = a 2 a b = a b
  12. (2+ 2 x+1 ) (3 6 x+2 ) (1+ 1 x ) =[ 2(x+1 ) +2 x+1 ] [ 3(x+2 ) 6 x+2 ] ( x+1 x ) =(2x+4 ) [ 3x+ 6 6 x+2 ] ( 1 x ) =2 (x+2 )( 3 x x+2 ) ( 1 x ) =6