Comparte esto 👍👍DESCARGACAPITULO XIV Operaciones con Fracciones Ejercicio 134Simplificar: x 2 3 y 2 ÷ 2x y 3 = x 2 3 y 2 2 x y 3 = xy 6 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 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 6 a 2 x 3 ÷ a 2 x 5 = 6 a 2 x a 2 x 5 =30 x 2 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 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 x–1 3 ÷ 2x–2 6 = x–1 3 2 (x–1 ) =1 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 ) 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 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 ) 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 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 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 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 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 ) 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 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 ) 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 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 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 ) 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 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 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 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 Categories: Capítulo XIV