Ejercicio 132

Gestor Baldor

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CAPITULO XIV

Operaciones con Fracciones

Ejercicio 132

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2 a 2 3b × 6 b 2 4a = 2 a 2 3b × 6 b 2 4 a =ab
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
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
5 a × 2a b 2 × 3b 10 = 5 a × 2 a b 2 × 3 b 10 = 3 b
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
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
2 x 2 +x 6 × 8 4x+2 = x ( 2x+1 ) × 2 ( 2x+1 ) = 2x 3
5x+25 14 × 7x+7 10x+50 = 5 ( x+5 ) × 7 ( x+1 ) ( x+5 ) = x+1 4
m+n mn– n 2 × n 2 m 2 – n 2 = ( m+n ) n ( m–n ) × n 2 ( m–n ) ( m+n ) = n ( m–n ) 2
xy–2 y 2 x 2 +xy × x 2 +2xy+ y 2 x 2 –2xy = y ( x–2y ) x ( x+y ) × ( x+y ) 2 x ( x–2y ) = y( x+y ) x 2
x 2 –4xy+4 y 2 x 2 +2xy × x 2 x 2 –4 y 2 = ( x–2y ) 2 x ( x+2y ) × x 2 ( x+2y ) ( x–2y ) = x( x–2y ) ( x+2y ) 2
2 x 2 +2x 2 x 2 × x 2 –3x x 2 –2x–3 = 2 x ( x+1 ) 2 x 2 × x ( x–3 ) ( x–3 ) ( x+1 ) =1
a 2 –ab+a–b a 2 +2a+1 × 3 6 a 2 –6ab = a( a–b ) +( a–b ) ( a+1 ) 2 × 3 6a( a–b ) = ( a–b ) ( a+1 ) ( a+1 ) 2 × 3 a ( a–b ) = 1 2( a+1 )
( x–y ) 3 x 3 –1 × x 2 +x+1 ( x–y ) 2 = ( x–y ) 3 ( x–1 ) ( x 2 +x+1 ) × x 2 +x+1 ( x–y ) 2 = x–y x–1
2a–2 2 a 2 –50 × a 2 –4a–5 3a+3 = 2 ( a–1 ) 2 ( a 2 –25 ) × ( a–5 ) ( a+1 ) 3 ( a+1 ) = a–1 ( a+5 ) ( a–5 ) × a–5 3 = a–1 3( a+5 )
2 x 2 –3x–2 6x+3 × 3x+6 x 2 –4 = 2 x 2 –4x+x–2 3( 2x+1 ) × 3 ( x+2 ) ( x–2 ) ( x+2 ) = 2x( x–2 ) +x–2 3( 2x+1 ) × 3 x–2 = ( 2x+1 ) ( x–2 ) 3 ( 2x+1 ) × 3 ( x–2 ) =1
y 2 +9y+18 y–5 × 5y–25 5y+15 = ( y+6 ) ( y+3 ) y–5 × 5 ( y–5 ) 5 ( y+3 ) =y+6
x 3 +2 x 2 –3x 4 x 2 +8x+3 × 2 x 2 +3x x 2 –x = x( x 2 +2x–3 ) 4 x 2 +2x+6x+3 × x ( 2x+3 ) x ( x–1 ) = x( x+3 ) ( x–1 ) 2x( 2x+1 ) +3( 2x+1 ) × 2x+3 x–1 = x( x+3 ) ( 2x+3 ) ( 2x+1 ) × ( 2x+3 ) = x( x+3 ) 2x+1
x 3 –27 a 3 –1 × a 2 +a+1 x 2 +3x+9 = ( x–3 ) ( x 2 +3x+9 ) ( a–1 ) ( a 2 +a+1 ) × a 2 +a+1 x 2 +3x+9 = x–3 a–1
a 2 +4ab+4 b 2 3 × 2a+4b ( a+2b ) 3 = ( a+2b ) 2 3 × 2 ( a+2b ) ( a+2b ) 3 = 2 3
1–x a+1 × a 2 +a x– x 2 × x 2 a = 1–x a+1 × a ( a+1 ) x ( 1–x ) × x 2 a =x
x 2 +2x x 2 –16 × x 2 –2x–8 x 3 + x 2 × x 2 +4x x 2 +4x+4 = x ( x+2 ) ( x–4 ) ( x+4 ) × x 2 –4x+2x–8 x 2 ( x+1 ) × x ( x+4 ) ( x+2 ) 2 = 1 x–4 × x( x–4 ) +2( x–4 ) x+1 × 1 x+2 = 1 x–4 × ( x–4 ) ( x+2 ) x+1 × 1 x+2 = 1 x+1
( m+n ) 2 – x 2 ( m+x ) 2 – n 2 × ( m–n ) 2 – x 2 m 2 +mn–mx = [ ( m+n ) –x ] [ ( m+n ) +x ] [ ( m+x ) –n ] [ ( m+x ) +n ] × [ ( m–n ) –x ] [ ( m–n ) +x ] m( m+n–x ) = [ m+n–x ] [ m+n+x ] [ m+x–n ] [ m+x+n ] × [ m–n–x ] [ m–n+x ] m ( m+n–x ) = m–n–x m
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 ( x–1 ) × x ( x 2 –1 ) x ( a 2 + b 2 ) × x x+1 = 1 x–1 × ( x–1 ) ( x+1 ) × 1 x+1 =1
a 2 –5a+6 3a–15 × 6a a 2 –a–30 × a 2 –25 2a–4 = ( a–3 ) ( a–2 ) 3 ( a–5 ) × 6 a ( a–6 ) ( a+5 ) × ( a+5 ) ( a–5 ) 2 ( a–2 ) = a( a–3 ) a–6
x 2 –3xy–10 y 2 x 2 –2xy–8 y 2 × x 2 –16 y 2 x 2 +4xy × x 2 –6xy x+2y = ( x–5y ) ( x+2y ) ( x–4y ) ( x+2y ) × ( x–4y ) ( x+4y ) x ( x+4y ) × x ( x–6y ) x+2y = ( x–5y ) ( x–6y ) x+2y
x 2 +4ax+4 a 2 3ax–6 a 2 × 2ax–4 a 2 ax+a × 6a+6x x 2 +3ax+2 a 2 = ( x+2a ) 2 3 a ( x–2a ) × 2 a ( x–2a ) a ( x+1 ) × ( a+x ) ( x+2a ) ( x+a ) = 4( x+2a ) a( x+1 )
a 2 –81 2 a 2 +10a × a+11 a 2 –36 × 2a–12 2a+18 × a 3 +5 a 2 2a+22 = ( a+9 ) ( a–9 ) 2 a ( a+5 ) × a+11 ( a–6 ) ( a+6 ) × 2 ( a–6 ) 2 ( a+9 ) × a 2 ( a+5 ) 2 ( a+11 ) = a( a–9 ) 4( a+6 )
a 2 +7a+10 a 2 –6a–7 × a 2 –3a–4 a 2 +2a–15 × a 3 –2 a 2 –3a a 2 –2a–8 = ( a+5 ) ( a+2 ) ( a–7 ) ( a+1 ) × ( a–4 ) ( a+1 ) ( a+5 ) ( a–3 ) × a( a 2 –2a–3 ) ( a–4 ) ( a+2 ) = 1 a–7 × 1 a–3 × a ( a–3 ) ( a+1 ) = a( a+1 ) a–7
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 x–3 = 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 x–3 = ( 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 x–3 = x+1 ( x+3 ) ( x–3 ) = x+1 x 2 –9