Comparte esto 👍👍DESCARGACAPITULO XIII Simplificación de fracciones Simplificación de fracciones cuyos términos sean polinomios. Caso en que hay que cambiar el signo a uno o más factores Ejercicio 120Simplificar o reducir a su más simple expresión: 4–4x 6x–6 =– 4x–4 6x–6 =– (x–1 ) (x–1 ) =– 2 3 a 2 – b 2 b 2 – a 2 =– a 2 – b 2 a 2 – b 2 =–1 m 2 – n 2 (n–m ) 2 =– n 2 – m 2 (n–m ) 2 =– (n–m )(n+m ) (n–m ) 2 =– n+m n–m x 2 –x–12 16– x 2 =– x 2 –x–12 x 2 –16 =– (x–4 )(x+3 ) (x–4 )(x+4 ) =– x+3 x+4 3y–6x 2mx–my–2nx+ny = 3(y–2x ) 2mx–2nx–my+ny = 3(y–2x ) 2x(m–n ) –y(m–n ) = 3(y–2x ) (m–n ) (2x–y ) = 3 (y–2x ) (n–m )(y–2x ) = 3 n–m 2 x 2 –9x–5 10+3x– x 2 =– 2 x 2 +x–10x–5 x 2 –3x–10 =– x(2x+1 ) –5(2x+1 ) (x–5 ) (x+2 ) =– (2x+1 )(x–5 ) (x–5 )(x+2 ) =– 2x+1 x+2 8– a 3 a 2 +2a–8 =– a 3 –8 a 2 +2a–8 =– (a–2 )( a 2 +2a+4 ) (a+4 )(a–2 ) =– a 2 +2a+4 a+4 a 2 +a–2 n–an–m+am = (a+2 ) (a–1 ) n–m–(an–am ) = (a+2 ) (a–1 ) n–m–a(n–m ) = (a+2 ) (a–1 ) (1–a ) (n–m ) = (a+2 )(a–1 ) (a–1 )(m–n ) = a+2 m–n 4 x 2 –4xy+ y 2 5y–10x = (2x–y ) 2 5(y–2x ) =– (2x–y ) 2 5 (2x–y ) =– 2x–y 5 3mx–nx–3my+ny n y 2 –n x 2 –3m y 2 +3m x 2 = 3mx–3my–(nx–ny ) (n y 2 –n x 2 ) –(3m y 2 –3m x 2 ) = 3m(x–y ) –n(x–y ) n( y 2 – x 2 ) –3m( y 2 – x 2 ) = (3m–n ) (x–y ) ( y 2 – x 2 ) (n–3m ) = (3m–n )(x–y ) ( x 2 – y 2 )(3m–n ) = x–y (x–y )(x+y ) = 1 x+y 9–6x+ x 2 x 2 –7x+12 = (3–x ) 2 (x–4 ) (x–3 ) = (3–x ) 2 (4–x )(3–x ) = 3–x 4–x a 2 – b 2 b 3 – a 3 = (a–b ) (a+b ) (b–a ) ( b 2 +ab+ a 2 ) =– (b–a )(a+b ) (b–a )( b 2 +ab+ a 2 ) =– a+b b 2 +ab+ a 2 3ax–3bx–6a+6b 2b–2a–bx+ax = 3x(a–b ) –6(a–b ) 2(b–a ) –x(b–a ) = (3x–6 ) (a–b ) (b–a ) (2–x ) = 3 (x–2 ) (a–b ) (a–b ) (x–2 ) =3 a 2 – x 2 x 2 –ax–3x+3a = (a–x ) (a+x ) x(x–a ) –3(x–a ) = (a–x ) (a+x ) (x–a ) (x–3 ) = (a–x )(a+x ) (a–x )(3–x ) = a+x 3–x 3bx–6x 8– b 3 = 3x(b–2 ) (2–b ) (4+2b+ b 2 ) =– 3x (b–2 ) (b–2 )(4+2b+ b 2 ) =– 3x 4+2b+ b 2 (1–a ) 3 a–1 =– (1–a ) 1–a =– (1–a ) 2 2 x 3 –2 x 2 y–2x y 2 3 y 3 +3x y 2 –3 x 2 y = 2x( x 2 –xy– y 2 ) 3y( y 2 +xy– x 2 ) =– 2x ( x 2 –xy– y 2 ) 3y ( x 2 –xy– y 2 ) =– 2x 3y (a–b ) 3 (b–a ) 2 = (a–b ) 3 (a–b ) 2 =a–b 2 x 2 –22x+60 75–3 x 2 = 2( x 2 –11x+30 ) 3(25– x 2 ) = 2(x–6 ) (x–5 ) 3(5–x ) (5+x ) = 2(6–x )(5–x ) 3 (5–x )(5+x ) = 2(6–x ) 3(5+x ) 6a n 2 –3 b 2 n 2 b 4 –4a b 2 +4 a 2 = 3 n 2 (2a– b 2 ) ( b 2 –2a ) 2 =– 3 n 2 ( b 2 –2a ) ( b 2 –2a ) 2 = 3 n 2 2a– b 2 (x–y ) 2 – z 2 (y+z ) 2 – x 2 = [(x–y ) –z ] [(x–y ) +z ] [(y+z ) –x ] [(y+z ) +x ] = (x–y–z ) (x–y+z ) (y+z–x ) (y+z+x ) = (y+z–x )(y–x–z ) (y+z–x )(y+z+x ) = y–x–z y+z+x 3 a 2 –3ab bd–ad–bc+ac = 3a(a–b ) d(b–a ) –c(b–a ) = 3a(a–b ) (d–c ) (b–a ) = 3a (a–b ) (c–d )(a–b ) = 3a c–d (x–5 ) 3 125– x 3 =– (x–5 ) 3 x 3 –125 =– (x–5 ) (x–5 )( x 2 +5x+25 ) =– (x–5 ) 2 x 2 +5x+25 13x–6–6 x 2 6 x 2 –13x+6 =– 6 x 2 –13x+6 6 x 2 –13x+6 =–1 2 x 3 –2x y 2 + x 2 – y 2 2x y 2 + y 2 –2 x 3 – x 2 = 2x( x 2 – y 2 ) +( x 2 – y 2 ) y 2 (2x+1 ) – x 2 (2x+1 ) = (2x+1 )( x 2 – y 2 ) ( y 2 – x 2 )(2x+1 ) =– x 2 – y 2 x 2 – y 2 =–1 30 x 2 y–45x y 2 –20 x 3 8 x 3 +27 y 3 = 5x(6xy–9 y 2 –4 x 2 ) (2x+3y ) (4 x 2 –6xy+9 y 2 ) =– 5x (4 x 2 –6xy+9 y 2 ) (2x+3y )(4 x 2 –6xy+9 y 2 ) =– 5x 2x+3y n+1– n 3 – n 2 n 3 –n–2 n 2 +2 = n+1– n 2 (n+1 ) n( n 2 –1 ) –2( n 2 –1 ) = (1– n 2 ) (n+1 ) ( n 2 –1 ) (n–2 ) = ( n 2 –1 )(n+1 ) ( n 2 –1 )(2–n ) = n+1 2–n (x–2 ) 2 ( x 2 +x–12 ) (2–x ) (3–x ) 2 = (2–x ) 2 (x+4 ) (x–3 ) (2–x ) (3–x ) 2 = (x–2 ) (x+4 )(3–x ) (3–x ) 2 = (x–2 ) (x+4 ) 3–x 5 x 3 –15 x 2 y 90 x 3 y 2 –10 x 5 = 5 x 2 (x–3y ) x 3 (9 y 2 – x 2 ) = x–3y 2x(3y–x ) (3y+x ) =– x–3y 2x (x–3y )(3y+x ) =– 1 2x(3y+x ) ( x 2 –1 ) ( x 2 –8x+16 ) ( x 2 –4x ) (1– x 2 ) = ( x 2 –1 )( x 2 –8x+16 ) (4x– x 2 )( x 2 –1 ) = (x–4 ) 2 x(4–x ) =– (x–4 ) 2 x (x–4 ) =– x–4 x = 4–x x Categories: Capítulo XIII