Comparte esto 👍👍DESCARGACAPITULO XIV Operaciones con Fracciones Ejercicio 127Simplificar: 1 a+1 + 1 a–1 = a– 1 +a+ 1 (a+1 ) (a–1 ) = 2a a 2 –1 2 x+4 + 1 x–3 = 2(x–3 ) +x+4 (x+4 ) (x–3 ) = 2x–6+x+4 (x+4 ) (x–3 ) = 3x–2 (x+4 ) (x–3 ) 3 1–x + 6 2x+5 = 3(2x+5 ) +6(1–x ) (1–x ) (2x+5 ) = 6x +15+6– 6x (1–x ) (2x+5 ) = 21 (1–x ) (2x+5 ) x x–y + x x+y = x(x+y ) +x(x–y ) (x–y ) (x+y ) = x[x+ y +x– y ] x 2 – y 2 = 2 x 2 x 2 – y 2 m+3 m–3 + m+2 m–2 = (m–2 ) (m+3 ) +(m+2 ) (m–3 ) (m–3 ) (m–2 ) = m 2 + m –6+ m 2 – m –6 (m–3 ) (m–2 ) = 2 m 2 –12 (m–3 ) (m–2 ) = 2( m 2 –6 ) (m–3 ) (m–2 ) x+y x–y + x–y x+y = (x+y ) 2 + (x–y ) 2 (x–y ) (x+y ) = x 2 + 2xy + y 2 + x 2 – 2xy + y 2 x 2 – y 2 = 2 x 2 +2 y 2 x 2 – y 2 = 2( x 2 + y 2 ) x 2 – y 2 x x 2 –1 + x+1 (x–1 ) 2 = x (x–1 ) (x+1 ) + x+1 (x–1 ) 2 = x(x–1 ) + (x+1 ) 2 (x+1 ) (x–1 ) 2 = x 2 –x+ x 2 +2x+1 (x+1 ) (x–1 ) 2 = 2 x 2 +x+1 (x+1 ) (x–1 ) 2 2 x–5 + 3x x 2 –25 = 2 x–5 + 3x (x–5 ) (x+5 ) = 2(x+5 ) +3x (x–5 ) (x+5 ) = 2x+10+3x (x–5 ) (x+5 ) = 5x+10 (x–5 ) (x+5 ) = 5(x+2 ) (x–5 ) (x+5 ) 1 3x–2y + x–y 9 x 2 –4 y 2 = 1 3x–2y + x–y (3x–2y ) (3x+2y ) = 3x+2y+x–y (3x–2y ) (3x+2y ) = 4x+y (3x–2y ) (3x+2y ) x+a x+3a + 3 a 2 – x 2 x 2 –9 a 2 = x+a x+3a + 3 a 2 – x 2 (x+3a ) (x–3a ) = (x+a ) (x–3a ) +3 a 2 – x 2 (x+3a ) (x–3a ) = x 2 –2ax– 3 a 2 + 3 a 2 – x 2 (x+3a ) (x–3a ) = –2ax x 2 –9 a 2 = 2ax 9 a 2 – x 2 a 1– a 2 + a 1+ a 2 =a[ 1+ a 2 +1– a 2 (1– a 2 ) (1+ a 2 ) ] =a[ 2 1– a 4 ] = 2a 1– a 4 2 a 2 –ab + 2 ab+ b 2 =2[ 1 a(a–b ) + 1 b(a+b ) ] =2[ b(a+b ) +a(a–b ) ab(a+b ) (a–b ) ] =2[ ab + b 2 + a 2 – ab ab( a 2 – b 2 ) ] = 2( a 2 + b 2 ) ab( a 2 – b 2 ) ab 9 a 2 – b 2 + a 3a+b =a[ b (3a+b ) (3a–b ) + 1 3a+b ] =a[ b +3a– b (3a+b ) (3a–b ) ] = 3 a 2 9 a 2 – b 2 1 a 2 – b 2 + 1 (a–b ) 2 = 1 (a+b ) (a–b ) + 1 (a–b ) 2 = a– b +a+ b (a+b ) (a–b ) 2 = 2a (a+b ) (a–b ) 2 3 x 2 + y 2 + 2 (x+y ) 2 = 3 (x+y ) 2 +2( x 2 + y 2 ) ( x 2 + y 2 ) (x+y ) 2 = 3( x 2 +2xy+ y 2 ) +2 x 2 +2 y 2 ( x 2 + y 2 ) (x+y ) 2 = 3 x 2 +6xy+3 y 2 +2 x 2 +2 y 2 ( x 2 + y 2 ) (x+y ) 2 = 5 x 2 +6xy+5 y 2 ( x 2 + y 2 ) (x+y ) 2 x a 2 –ax + a+x ax + a ax– x 2 = x a(a–x ) + a+x ax + a x(a–x ) = x 2 +(a+x ) (a–x ) + a 2 ax(a–x ) = x 2 + a 2 – x 2 + a 2 ax(a–x ) = 2 a 2 a x(a–x ) = 2a x(a–x ) 3 2x+4 + x–1 2x–4 + x+8 x 2 –4 = 3 2(x+2 ) + x–1 2(x–2 ) + x+8 (x+2 ) (x–2 ) = 3(x–2 ) +(x–1 ) (x+2 ) +2(x+8 ) 2(x+2 ) (x–2 ) = 3x–6+ x 2 +x–2+2x+16 2(x+2 ) (x–2 ) = x 2 +6x+8 2(x+2 ) (x–2 ) = (x+4 )(x+2 ) 2 (x+2 )(x–2 ) = x+4 2(x–2 ) 1 x+ x 2 + 1 x– x 2 + x+3 1– x 2 = 1 x(1+x ) + 1 x(1–x ) + x+3 (1–x ) (1+x ) = 1– x +1+ x +x(x+3 ) x(1–x ) (1+x ) = 2+ x 2 +3x x(1–x ) (1+x ) = x 2 +3x+2 x(1–x ) (1+x ) = (x+2 )(x+1 ) x(1–x )(x+1 ) = x+2 x(1–x ) x–y x+y + x+y x–y + 4xy x 2 – y 2 = x–y x+y + x+y x–y + 4xy (x+y ) (x–y ) = (x–y ) 2 + (x+y ) 2 +4xy (x+y ) (x–y ) = x 2 – 2xy + y 2 + x 2 + 2xy + y 2 +4xy (x+y ) (x–y ) = 2 x 2 +4xy+2 y 2 (x+y ) (x–y ) = 2( x 2 +2xy+ y 2 ) (x+y ) (x–y ) = 2 (x+y ) 2 (x+y )(x–y ) = 2(x+y ) x–y 1 a–5 + a a 2 –4a–5 + a+5 a 2 +2a+1 = 1 a–5 + a (a–5 ) (a+1 ) + a+5 (a+1 ) 2 = (a+1 ) 2 +a(a+1 ) +(a+5 ) (a–5 ) (a–5 ) (a+1 ) 2 = a 2 +2a+1+ a 2 +a+ a 2 –25 (a–5 ) (a+1 ) 2 = 3 a 2 +3a–24 (a–5 ) (a+1 ) 2 = 3( a 2 +a–8 ) (a–5 ) (a+1 ) 2 3 a + 2 5a–3 + 1–85a 25 a 2 –9 = 3 a + 2 5a–3 + 1–85a (5a–3 ) (5a+3 ) = 3(5a–3 ) (5a+3 ) +2a(5a+3 ) +a(1–85a ) a(5a–3 ) (5a+3 ) = 3(25 a 2 –9 ) +10 a 2 +6a+a–85 a 2 a(5a–3 ) (5a+3 ) = 75 a 2 –27+7a– 75 a 2 a(25 a 2 –9 ) = 7a–27 a(25 a 2 –9 ) x+1 10 + x–3 5x–10 + x–2 2 = x+1 10 + x–3 5(x–2 ) + x–2 2 = (x+1 ) (x–2 ) +2(x–3 ) +5 (x–2 ) 2 10(x–2 ) = x 2 –x–2+2x–6+5( x 2 –4x+4 ) 10(x–2 ) = x 2 +x–8+5 x 2 –20x+20 10(x–2 ) = 6 x 2 –19x+12 10(x–2 ) x+5 x 2 +x–12 + x+4 x 2 +2x–15 + x–3 x 2 +9x+20 = x+5 (x+4 ) (x–3 ) + x+4 (x+5 ) (x–3 ) + x–3 (x+5 ) (x+4 ) = (x+5 ) 2 + (x+4 ) 2 + (x–3 ) 2 (x+4 ) (x–3 ) (x+5 ) = x 2 +10x+25+ x 2 +8x+16+ x 2 –6x+9 (x+4 ) (x–3 ) (x+5 ) = 3 x 2 +12x+50 (x+4 ) (x–3 ) (x+5 ) 1 x–2 + 1–2 x 2 x 3 –8 + x x 2 +2x+4 = 1 x–2 + 1–2 x 2 (x–2 ) ( x 2 +2x+4 ) + x x 2 +2x+4 = x 2 +2x+4+1–2 x 2 +x(x–2 ) (x–2 ) ( x 2 +2x+4 ) = x 2 + 2x +4+1– 2 x 2 + x 2 – 2x x 3 –8 = 5 x 3 –8 2 a+1 + a (a+1 ) 2 + a+1 (a+1 ) 3 = 1 a+1 [2+ a a+1 + a+1 (a+1 ) 2 ] = 1 a+1 [ 2 (a+1 ) 2 +a(a+1 ) +a+1 (a+1 ) 2 ] = 1 a+1 [ 2( a 2 +2a+1 ) + a 2 +a+a+1 (a+1 ) 2 ] = 1 a+1 [ 2 a 2 +4a+2+ a 2 +2a+1 (a+1 ) 2 ] = 1 a+1 [ 3 a 2 +6a+3 (a+1 ) 2 ] = 3 a+1 [ a 2 +2a+1 (a+1 ) 2 ] = 3 a+1 [ (a+1 ) 2 (a+1 ) 2 ] = 3 a+1 2x 3 x 2 +11x+6 + x+1 x 2 –9 + 1 3x+2 = 2x 3 x 2 +9x+2x+6 + x+1 (x–3 ) (x+3 ) + 1 3x+2 = 2x 3x(x+3 ) +2(x+3 ) + x+1 (x–3 ) (x+3 ) + 1 3x+2 = 2x (3x+2 ) (x+3 ) + x+1 (x–3 ) (x+3 ) + 1 3x+2 = 2x(x–3 ) +(x+1 ) (3x+2 ) +(x+3 ) (x–3 ) (3x+2 ) (x+3 ) (x–3 ) = 6 x 2 –x–7 (3x+2 ) (x+3 ) (x–3 ) x 2 –4 x 3 +1 + 1 x+1 + 3 x 2 –x+1 = x 2 –4 (x+1 ) ( x 2 –x+1 ) + 1 x+1 + 3 x 2 –x+1 = x 2 –4+ x 2 –x+1+3(x+1 ) (x+1 ) ( x 2 –x+1 ) = 2 x 2 – 4 –x+ 1 +3x+ 3 (x+1 ) ( x 2 –x+1 ) = 2 x 2 +2x (x+1 ) ( x 2 –x+1 ) = 2x (x+1 ) (x+1 )( x 2 –x+1 ) = 2x x 2 –x+1 1 x–1 + 1 (x–1 ) (x+2 ) + x+1 (x–1 ) (x+2 ) (x+3 ) = 1 x–1 [1+ 1 x+2 + x+1 (x+2 ) (x+3 ) ] = 1 x–1 [ (x+2 ) (x+3 ) +x+3+x+1 (x+2 ) (x+3 ) ] = 1 x–1 [ x 2 +5x+6+2x+4 (x+2 ) (x+3 ) ] = 1 x–1 [ x 2 +7x+10 (x+2 ) (x+3 ) ] = 1 x–1 [ (x+2 )(x+5 ) (x+2 )(x+3 ) ] = x+5 (x–1 ) (x+3 ) x–2 2 x 2 –5x–3 + x–3 2 x 2 –3x–2 + 2x–1 x 2 –5x+6 = x–2 2 x 2 +x–6x–3 + x–3 2 x 2 –4x+x–2 + 2x–1 (x–3 ) (x–2 ) = x–2 x(2x+1 ) –3(2x+1 ) + x–3 2x(x–2 ) +(x–2 ) + 2x–1 (x–3 ) (x–2 ) = x–2 (x–3 ) (2x+1 ) + x–3 (2x+1 ) (x–2 ) + 2x–1 (x–3 ) (x–2 ) = (x–2 ) 2 + (x–3 ) 2 +(2x+1 ) (2x–1 ) (x–3 ) (2x+1 ) (x–2 ) = x 2 –4x+4+ x 2 –6x+9+4 x 2 –1 (x–3 ) (2x+1 ) (x–2 ) = 6 x 2 –10x+12 (x–3 ) (2x+1 ) (x–2 ) = 2(3 x 2 –5x+6 ) (x–3 ) (2x+1 ) (x–2 ) a–2 a–1 + a+3 a+2 + a+1 a–3 = (a–2 ) (a+2 ) (a–3 ) +(a–1 ) (a–3 ) (a+3 ) +(a–1 ) (a+1 ) (a+2 ) (a–1 ) (a+2 ) (a–3 ) = ( a 2 –4 ) (a–3 ) +(a–1 ) ( a 2 –9 ) +( a 2 –1 ) (a+2 ) (a–1 ) (a+2 ) (a–3 ) = a 3 –4a–3 a 2 +12+ a 3 –9a– a 2 +9+ a 3 +2 a 2 –a–2 (a–1 ) (a+2 ) (a–3 ) = 3 a 3 –2 a 2 –14a+19 (a–1 ) (a+2 ) (a–3 ) Categories: Capítulo XIV