Comparte esto 👍👍DESCARGACAPITULO XIV Operaciones con Fracciones Ejercicio 130Simplificar: 2 x–3 + 3 x+2 – 4x–7 x 2 –x–6 = 2 x–3 + 3 x+2 – 4x–7 (x–3 ) (x+2 ) = 2(x+2 ) +3(x–3 ) –(4x–7 ) (x–3 ) (x+2 ) = 2x+4+3x–9–4x+7 (x–3 ) (x+2 ) = x+2 (x–3 )(x+2 ) = 1 x–3 a 3a+6 – 1 6a+12 + a+12 12a+24 = a 3(a+2 ) – 1 6(a+2 ) + a+12 12(a+2 ) = 1 3(a+2 ) [a– 1 2 + a+12 4 ] = 1 3(a+2 ) [ 4a–2+a+12 4 ] = 1 3(a+2 ) [ 5a+10 4 ] = 1 3 (a+2 ) [ 5 (a+2 ) 4 ] = 5 12 x x 2 +1 + 1 3x – 1 x 2 = 3 x 3 +x( x 2 +1 ) –3( x 2 +1 ) 3 x 2 ( x 2 +1 ) = 3 x 3 + x 3 +x–3 x 2 –3 3 x 2 ( x 2 +1 ) = 4 x 3 –3 x 2 +x–3 3 x 2 ( x 2 +1 ) a+3 a 2 –1 + a–1 2a+2 + a–4 4a–4 = a+3 (a–1 ) (a+1 ) + a–1 2(a+1 ) + a–4 4(a–1 ) = 4(a+3 ) +2 (a–1 ) 2 +(a+1 ) (a–4 ) 4(a–1 ) (a+1 ) = 4a+12+2( a 2 –2a+1 ) + a 2 –3a–4 4(a–1 ) (a+1 ) = a+8+2 a 2 –4a+2+ a 2 4( a 2 –1 ) = 3 a 2 –3a+10 4( a 2 –1 ) a–b a 2 +ab + a+b ab – a ab+ b 2 = a–b a(a+b ) + a+b ab – a b(a+b ) = b(a–b ) + (a+b ) 2 – a 2 ab(a+b ) = ab– b 2 + a 2 +2ab+ b 2 – a 2 ab(a+b ) = 3 ab ab (a+b ) = 3 a+b x–y x+y – x+y x–y + 4 x 2 x 2 – y 2 = x–y x+y – x+y x–y + 4 x 2 (x+y ) (x–y ) = (x–y ) 2 – (x+y ) 2 +4 x 2 (x+y ) (x–y ) = [(x–y ) +(x+y ) ] [(x–y ) –(x+y ) ] +4 x 2 (x+y ) (x–y ) = [x– y +x+ y ] [ x –y– x –y ] +4 x 2 (x+y ) (x–y ) = 2x(–2y ) +4 x 2 (x+y ) (x–y ) = 4 x 2 –4xy (x+y ) (x–y ) = 4x (x–y ) (x+y )(x–y ) = 4x x+y x a 2 –ax + 1 a + 1 x = x a(a–x ) + 1 a + 1 x = x 2 +x(a–x ) +a(a–x ) ax(a–x ) = x 2 + ax – x 2 + a 2 – ax ax(a–x ) = a 2 a x(a–x ) = a x(a–x ) x+1 x 2 –x–20 – x+4 x 2 –4x–5 + x+5 x 2 +5x+4 = x+1 (x–5 ) (x+4 ) – x+4 (x–5 ) (x+1 ) + x+5 (x+4 ) (x+1 ) = (x+1 ) 2 – (x+4 ) 2 +(x–5 ) (x+5 ) (x+1 ) (x–5 ) (x+4 ) = [(x+1 ) +(x+4 ) ] [(x+1 ) –(x+4 ) ] + x 2 –25 (x+1 ) (x–5 ) (x+4 ) = [x+1+x+4 ] [ x +1– x –4 ] + x 2 –25 (x+1 ) (x–5 ) (x+4 ) = –3(2x+5 ) + x 2 –25 (x+1 ) (x–5 ) (x+4 ) = –6x–15+ x 2 –25 (x+1 ) (x–5 ) (x+4 ) = x 2 –6x–40 (x+1 ) (x–5 ) (x+4 ) = (x–10 )(x+4 ) (x+1 ) (x–5 )(x+4 ) = x–10 (x+1 ) (x–5 ) 2x+1 12x+8 – x 2 6 x 2 +x–2 + 2x 16x–8 = 2x+1 4(3x+2 ) – x 2 6 x 2 –3x+4x–2 + 2x 8(2x–1 ) = 2x+1 4(3x+2 ) – x 2 3x(2x–1 ) +2(2x–1 ) + 2x 8(2x–1 ) = 2x+1 4(3x+2 ) – x 2 (3x+2 ) (2x–1 ) + 2x 8(2x–1 ) = 2(2x–1 ) (2x+1 ) –8 x 2 +2x(3x+2 ) 8(3x+2 ) (2x–1 ) = 2(4 x 2 –1 ) –8 x 2 +6 x 2 +4x 8(3x+2 ) (2x–1 ) = 8 x 2 –2–2 x 2 +4x 8(3x+2 ) (2x–1 ) = 6 x 2 +4x–2 8(3x+2 ) (2x–1 ) = 2 (3 x 2 +2x–1 ) (3x+2 ) (2x–1 ) = 3 x 2 +2x–1 4(3x+2 ) (2x–1 ) 1 ax – 1 a 2 +ax + 1 a+x = 1 ax – 1 a(a+x ) + 1 a+x = a+ x – x +ax ax(a+x ) = a+ax ax(a+x ) = a (1+x ) a x(a+x ) = 1+x x(a+x ) 1 x+y – 1 x–y + 2y x 2 + y 2 = (x–y ) ( x 2 + y 2 ) –(x+y ) ( x 2 + y 2 ) +2y(x+y ) (x–y ) (x+y ) (x–y ) ( x 2 + y 2 ) = x 3 +x y 2 – x 2 y– y 3 –( x 3 +x y 2 + x 2 y+ y 3 ) +2y( x 2 – y 2 ) (x+y ) (x–y ) ( x 2 + y 2 ) = x 3 + x y 2 – x 2 y – y 3 – x 3 – x y 2 – x 2 y – y 3 + 2 x 2 y –2 y 3 ( x 2 – y 2 ) ( x 2 + y 2 ) = –4 y 3 x 4 – y 4 = 4 y 3 y 4 – x 4 a–1 3a+3 – a–2 6a–6 + a 2 +2a–6 9 a 2 –9 = a–1 3(a+1 ) – a–2 6(a–1 ) + a 2 +2a–6 9( a 2 –1 ) = 1 3 [ a–1 a+1 – a–2 2(a–1 ) + a 2 +2a–6 3(a–1 ) (a+1 ) ] = 1 3 [ 6 (a–1 ) 2 –3(a–2 ) (a+1 ) +2( a 2 +2a–6 ) 6(a–1 ) (a+1 ) ] = 1 3 [ 6( a 2 –2a+1 ) –3( a 2 –a–2 ) +2 a 2 +4a–12 6(a–1 ) (a+1 ) ] = 1 3 [ 6 a 2 –12a+ 6 –3 a 2 +3a+ 6 +2 a 2 +4a– 12 6(a–1 ) (a+1 ) ] = 1 3 [ 5 a 2 –5a 6(a–1 ) (a+1 ) ] = 1 3 [ 5a (a–1 ) 6 (a–1 )(a+1 ) ] = 5a 18(a+1 ) 1 a 2 +2a–24 + 2 a 2 –2a–8 – 3 a 2 +8a+12 = 1 (a+6 ) (a–4 ) + 2 (a–4 ) (a+2 ) – 3 (a+6 ) (a+2 ) = a+2+2(a+6 ) –3(a–4 ) (a+6 ) (a–4 ) (a+2 ) = a +2+ 2a +12– 3a +12 (a+6 ) (a–4 ) (a+2 ) = 26 (a+6 ) (a–4 ) (a+2 ) x+y xy – x+2y xy+ y 2 – y x 2 +xy = x+y xy – x+2y y(x+y ) – y x(x+y ) = (x+y ) 2 –x(x+2y ) – y 2 xy(x+y ) = x 2 + 2xy + y 2 – x 2 – 2xy – y 2 xy(x+y ) =0 a 3 a 3 +1 + a+3 a 2 –a+1 – a–1 a+1 = a 3 (a+1 ) ( a 2 –a+1 ) + a+3 a 2 –a+1 – a–1 a+1 = a 3 +(a+3 ) (a+1 ) –(a–1 ) ( a 2 –a+1 ) (a+1 ) ( a 2 –a+1 ) = a 3 + a 2 +4a+3–( a 3 – a 2 +a– a 2 +a–1 ) (a+1 ) ( a 2 –a+1 ) = a 3 + a 2 +4a+3– a 3 +2 a 2 –2a+1 a 3 +1 = 3 a 2 +2a+4 a 3 +1 1 x–1 + 2x x 2 –1 – 3 x 2 x 3 –1 = 1 x–1 + 2x (x–1 ) (x+1 ) – 3 x 2 (x–1 ) ( x 2 +x+1 ) = 1 x–1 [1+ 2x x+1 – 3 x 2 x 2 +x+1 ] = 1 x–1 [ (x+1 ) ( x 2 +x+1 ) +2x( x 2 +x+1 ) –3 x 2 (x+1 ) (x+1 ) ( x 2 +x+1 ) ] = 1 x–1 [ x 3 + x 2 +x+ x 2 +x+1+ 2 x 3 + 2 x 2 +2x– 3 x 3 – 3 x 2 (x+1 ) ( x 2 +x+1 ) ] = 1 x–1 [ x 2 +4x+1 (x+1 ) ( x 2 +x+1 ) ] = x 2 +4x+1 (x+1 ) ( x 3 –1 ) a+b a 2 –ab+ b 2 – 1 a+b + 3 a 2 a 3 + b 3 = a+b a 2 –ab+ b 2 – 1 a+b + 3 a 2 (a+b ) ( a 2 –ab+ b 2 ) = (a+b ) 2 –( a 2 –ab+ b 2 ) +3 a 2 (a+b ) ( a 2 –ab+ b 2 ) = a 2 +2ab+ b 2 – a 2 +ab– b 2 +3 a 2 (a+b ) ( a 2 –ab+ b 2 ) = 3 a 2 +3ab (a+b ) ( a 2 –ab+ b 2 ) = 3a (a+b ) (a+b )( a 2 –ab+ b 2 ) = 3a a 2 –ab+ b 2 2 x–2 + 2x+3 x 2 +2x+4 – 6x+12 x 3 –8 = 2 x–2 + 2x+3 x 2 +2x+4 – 6x+12 (x–2 ) ( x 2 +2x+4 ) = 2( x 2 +2x+4 ) +(x–2 ) (2x+3 ) –(6x+12 ) (x–2 ) ( x 2 +2x+4 ) = 2 x 2 + 4x +8+2 x 2 +3x– 4x –6–6x–12 (x–2 ) ( x 2 +2x+4 ) = 4 x 2 –3x–10 (x–2 ) ( x 2 +2x+4 ) = 4 x 2 –8x+5x–10 (x–2 ) ( x 2 +2x+4 ) = 4x(x–2 ) +5(x–2 ) (x–2 ) ( x 2 +2x+4 ) = (4x+5 )(x–2 ) (x–2 )( x 2 +2x+4 ) = 4x+5 x 2 +2x+4 3x+2 x 2 +3x–10 – 5x+1 x 2 +4x–5 + 4x–1 x 2 –3x+2 = 3x+2 (x+5 ) (x–2 ) – 5x+1 (x+5 ) (x–1 ) + 4x–1 (x–2 ) (x–1 ) = (3x+2 ) (x–1 ) –(x–2 ) (5x+1 ) +(x+5 ) (4x–1 ) (x+5 ) (x–2 ) (x–1 ) = 3 x 2 + 2x –3x+2–5 x 2 – x +10x+2+4 x 2 – x +20x–5 (x+5 ) (x–2 ) (x–1 ) = 2 x 2 +27x–1 (x+5 ) (x–2 ) (x–1 ) 1 (n–1 ) 2 + 1 n–1 – 1 (n–1 ) 3 – 1 n = 1 (n–1 ) 2 + 1 n–1 – 1 (n–1 ) 3 – 1 n = n(n–1 ) +n (n–1 ) 2 –n– (n–1 ) 3 n (n–1 ) 3 = n 2 –n+n( n 2 –2n+1 ) –n–( n 3 –3 n 2 +3n–1 ) n (n–1 ) 3 = n 2 –2n+ n 3 –2 n 2 +n– n 3 +3 n 2 –3n+1 n (n–1 ) 3 = 2 n 2 –4n+1 n (n–1 ) 3 1 a 2 +5 – a 2 –5 ( a 2 +5 ) 2 + a 2 +5 a 4 –25 = 1 a 2 +5 – a 2 –5 ( a 2 +5 ) 2 + a 2 +5 ( a 2 +5 ) ( a 2 –5 ) = 1 a 2 +5 [1– a 2 –5 a 2 +5 + a 2 +5 a 2 –5 ] = 1 a 2 +5 [ ( a 2 +5 ) ( a 2 –5 ) – ( a 2 –5 ) 2 + ( a 2 +5 ) 2 ( a 2 +5 ) ( a 2 –5 ) ] = 1 a 2 +5 [ a 4 – 25 –( a 4 –10 a 2 +25 ) + a 4 +10 a 2 + 25 ( a 2 +5 ) ( a 2 –5 ) ] = 1 a 2 +5 [ 2 a 4 – a 4 +10 a 2 –25+10 a 2 ( a 2 +5 ) ( a 2 –5 ) ] = 1 a 2 +5 [ a 4 +20 a 2 –25 ( a 2 +5 ) ( a 2 –5 ) ] = a 4 +20 a 2 –25 ( a 2 +5 ) ( a 4 –25 ) 1– x 2 9– x 2 – x 2 9+6x+ x 2 – 6x 9–6x+ x 2 = 1– x 2 (3–x ) (3+x ) – x 2 (3+x ) 2 – 6x (3–x ) 2 = (1– x 2 ) (3–x ) (3+x ) – x 2 (3–x ) 2 –6x (3+x ) 2 (3–x ) 2 (3+x ) 2 = (1– x 2 ) (9– x 2 ) – x 2 (9–6x+ x 2 ) –6x(9+6x+ x 2 ) (3–x ) 2 (3+x ) 2 = 9– x 2 –9 x 2 + x 4 –9 x 2 + 6 x 3 – x 4 –54x–36 x 2 – 6 x 3 (3–x ) 2 (3+x ) 2 = 9–54x–55 x 2 (3–x ) 2 (3+x ) 2 x 2x+2 – x+1 3x–3 + x–1 6x+6 – 5 18x–18 = x 2(x+1 ) – x+1 3(x–1 ) + x–1 6(x+1 ) – 5 18(x–1 ) = 9x(x–1 ) –6 (x+1 ) 2 +3 (x–1 ) 2 –5(x+1 ) 18(x–1 ) (x+1 ) = 9 x 2 –9x–6( x 2 +2x+1 ) +3( x 2 –2x+1 ) –5x–5 18(x–1 ) (x+1 ) = 9 x 2 –9x–6 x 2 –12x–6+3 x 2 –6x+3–5x–5 18(x–1 ) (x+1 ) = 6 x 2 –32x–8 18(x–1 ) (x+1 ) = 2 (3 x 2 –16x–4 ) (x–1 ) (x+1 ) = 3 x 2 –16x–4 9(x–1 ) (x+1 ) a+2 2a+2 – 7a 8 a 2 –8 – a–3 4a–4 = a+2 2(a+1 ) – 7a 8( a 2 –1 ) – a–3 4(a–1 ) = 1 2 [ a+2 a+1 – 7a 4(a+1 ) (a–1 ) – a–3 2(a–1 ) ] = 1 2 [ 4(a+2 ) (a–1 ) –7a–2(a–3 ) (a+1 ) 4(a+1 ) (a–1 ) ] = 1 2 [ 4( a 2 +a–2 ) –7a–2( a 2 –2a–3 ) 4(a+1 ) (a–1 ) ] = 1 2 [ 4 a 2 +4a–8–7a–2 a 2 +4a+6 4(a+1 ) (a–1 ) ] = 1 2 [ 2 a 2 +a–2 4(a+1 ) (a–1 ) ] = 2 a 2 +a–2 8(a+1 ) (a–1 ) a–3 20a+10 + 2a+5 40a+20 – 4a–1 60a+30 = a–3 10(2a+1 ) + 2a+5 20(2a+1 ) – 4a–1 30(2a+1 ) = 1 10(2a+1 ) [a–3+ 2a+5 2 – 4a–1 3 ] = 1 10(2a+1 ) [ 6a–18+3(2a+5 ) –2(4a–1 ) 6 ] = 1 10(2a+1 ) [ 6a–18+6a+15–8a+2 6 ] = 1 10(2a+1 ) [ 4a–1 6 ] = 4a–1 60(2a+1 ) 2 2 x 2 +5x+3 – 1 2 x 2 –x–6 + 3 x 2 –x–2 = 2 2 x 2 +2x+3x+3 – 1 2 x 2 –4x+3x–6 + 3 (x–2 ) (x+1 ) = 2 2x(x+1 ) +3(x+1 ) – 1 2x(x–2 ) +3(x–2 ) + 3 (x–2 ) (x+1 ) = 2 (2x+3 ) (x+1 ) – 1 (2x+3 ) (x–2 ) + 3 (x–2 ) (x+1 ) = 2(x–2 ) –(x+1 ) +3(2x+3 ) (2x+3 ) (x+1 ) (x–2 ) = 2x–4–x–1+6x+9 (2x+3 ) (x+1 ) (x–2 ) = 7x+4 (2x+3 ) (x+1 ) (x–2 ) a–1 a–2 – a–2 a+3 + 1 a–1 = (a+3 ) (a–1 ) 2 – (a–2 ) 2 (a–1 ) +(a–2 ) (a+3 ) (a–2 ) (a+3 ) (a–1 ) = (a+3 ) ( a 2 –2a+1 ) –( a 2 –4a+4 ) (a–1 ) + a 2 +a–6 (a–2 ) (a+3 ) (a–1 ) = a 3 –2 a 2 +a+3 a 2 –6a+3–( a 3 –4 a 2 +4a– a 2 +4a–4 ) + a 2 +a–6 (a–2 ) (a+3 ) (a–1 ) = a 3 + a 2 –5a+3– a 3 +5 a 2 –8a+4+ a 2 +a–6 (a–2 ) (a+3 ) (a–1 ) = 7 a 2 –12a+1 (a–2 ) (a+3 ) (a–1 ) 2+3a 2–3a – 2–3a 2+3a – a (2–3a ) 2 = (2+3a ) 2 (2–3a ) – (2–3a ) 3 –a(2+3a ) (2+3a ) (2–3a ) 2 = (2+3a ) (4–9 a 2 ) –(8–36a+54 a 2 –27 a 3 ) –2a–3 a 2 (2+3a ) (2–3a ) 2 = 8 –18 a 2 +12a– 27 a 3 – 8 +36a–54 a 2 + 27 a 3 –2a–3 a 2 (2+3a ) (2–3a ) 2 = 46a–75 a 2 (2+3a ) (2–3a ) 2 1 5+5a + 1 5–5a – 1 10+10 a 2 = 1 5(1+a ) + 1 5(1–a ) – 1 10(1+ a 2 ) = 1 5 [ 1 1+a + 1 1–a – 1 2(1+ a 2 ) ] = 1 5 [ 2(1+ a 2 ) (1–a ) +2(1+ a 2 ) (1+a ) –(1–a ) (1+a ) 2(1+ a 2 ) (1–a ) (1+a ) ] = 1 5 [ 2(1+ a 2 –a– a 3 ) +2(1+ a 2 +a+ a 3 ) –(1– a 2 ) 2(1+ a 2 ) (1–a ) (1+a ) ] = 1 5 [ 2+2 a 2 – 2a – 2 a 3 +2+2 a 2 + 2a + 2 a 3 –1+ a 2 2(1+ a 2 ) (1– a 2 ) ] = 1 5 [ 5 a 2 +3 2(1+ a 2 ) (1– a 2 ) ] = 5 a 2 +3 10(1– a 4 ) 1 3–3x – 1 3+3x + x 6+6 x 2 – x 2–2 x 2 = 1 3(1–x ) – 1 3(1+x ) + x 6(1+ x 2 ) – x 2(1– x 2 ) = 2(1+ x 2 ) (1+x ) –2(1+ x 2 ) (1–x ) +x(1–x ) (1+x ) –3x(1+ x 2 ) 6(1+ x 2 ) (1–x ) (1+x ) = 2(1+ x 2 +x+ x 3 ) –2(1+ x 2 –x– x 3 ) +x(1– x 2 ) –3x–3 x 3 6(1+ x 2 ) (1– x 2 ) = 2 + 2 x 2 +2x+ 2 x 3 – 2 – 2 x 2 + 2x + 2 x 3 + x – x 3 – 3x – 3 x 3 6(1– x 4 ) = 2x 6(1– x 4 ) = 2 x (1– x 4 ) = x 3(1– x 4 ) Categories: Capítulo XIV