Ejercicio 128

Ejercicio 128

1. x–3 4 – x+2 8 = 1 4 [ x–3– x+2 2 ] = 1 4 [ 2( x–3 ) –( x+2 ) 2 ] = 1 4 [ 2x–6–x–2 2 ] = 1 4 [ x–8 2 ] = x–8 8
2. a+5b a 2 – b–3 ab = 1 a [ a+5b a – b–3 b ] = 1 a [ b( a+5b ) –a( b–3 ) ab ] = 1 a [ ab +5 b 2 – ab +3a ab ] = 1 a [ 3a+5 b 2 ab ] = 3a+5 b 2 a 2 b
3. 2 3m n 2 – 1 2 m 2 n = 1 mn [ 2 3n – 1 2m ] = 1 mn [ 2( 2m ) –3n 6mn ] = 1 mn [ 4m–3n 6mn ] = 4m–3n 6 m 2 n 2
4. a–3 5ab – 4–3a b 2 3 a 2 b 3 = 1 ab [ a–3 5 – 4–3a b 2 3a b 2 ] = 1 ab [ 3a b 2 ( a–3 ) –5( 4–3a b 2 ) 15a b 2 ] = 1 ab [ 3 a 2 b 2 –9a b 2 –20+15a b 2 15a b 2 ] = 1 ab [ 3 a 2 b 2 +6a b 2 –20 15a b 2 ] = 3 a 2 b 2 +6a b 2 –20 15 a 2 b 3
5. 2a+3 4a – a–2 8a = 1 4a [ 2a+3– a–2 2 ] = 1 4a [ 2( 2a+3 ) –( a–2 ) 2 ] = 1 4a [ 4a+6–a+2 2 ] = 1 4a [ 3a+8 2 ] = 3a+8 8a
6. y–2x 20x – x–3y 24y = 1 4 [ y–2x 5x – x–3y 6y ] = 1 4 [ 6y( y–2x ) –5x( x–3y ) 30xy ] = 1 4 [ 6 y 2 –12xy–5 x 2 +15xy 30xy ] = 1 4 [ 6 y 2 +3xy–5 x 2 30xy ] = 6 y 2 +3xy–5 x 2 120xy
7. x–1 3 – x–2 4 – x+3 6 = 4( x–1 ) –3( x–2 ) –2( x+3 ) 12 = 4x–4–3x+ 6 –2x– 6 12 = –x–4 12 =– x+4 12
8. 3 5 – 2a+1 10a – 4 a 2 +1 20 a 2 = 1 5 [ 3– 2a+1 2a – 4 a 2 +1 4 a 2 ] = 1 5 [ 12 a 2 –2a( 2a+1 ) –( 4 a 2 +1 ) 4 a 2 ] = 1 5 [ 12 a 2 –4 a 2 –2a–4 a 2 –1 4 a 2 ] = 1 5 [ 4 a 2 –2a–1 4 a 2 ] = 4 a 2 –2a–1 20 a 2
9. 3 5x – x–1 3 x 2 – x 2 +2x+3 15 x 3 = 1 x [ 3 5 – x–1 3x – x 2 +2x+3 15 x 2 ] = 1 x [ 9 x 2 –5x( x–1 ) –( x 2 +2x+3 ) 15 x 2 ] = 1 x [ 9 x 2 –5 x 2 +5x– x 2 –2x–3 15 x 2 ] = 1 x [ 3 x 2 +3x–3 15 x 2 ] = 3 ( x 2 +x–1 ) x 3 = x 2 +x–1 5 x 3
10. 1 2a – 2+b 3ab – 5 6 a 2 b 3 = 1 a [ 1 2 – 2+b 3b – 5 6a b 3 ] = 1 a [ 3a b 3 –2a b 2 ( 2+b ) –5 6a b 3 ] = 1 a [ 3a b 3 –4a b 2 –2a b 3 –5 6a b 3 ] = 1 a [ a b 3 –4a b 2 –5 6a b 3 ] = a b 3 –4a b 2 –5 6 a 2 b 3