Ejercicio 136

Ejercicio 136

1. 3x 4y × 8y 9x ÷ z 2 3 x 2 = 3 x 4 y × y 9 x × 3 x 2 z 2 = 2 x 2 z 2
2. 5a b ÷ ( 2a b 2 × 5x 4 a 2 ) = 5a b ÷ ( 2 a b 2 × 5x a 2 ) = 5a b ÷ 5x 2a b 2 = 5 a b × 2a b 2 5 x = 2 a 2 b x
3. a+1 a–1 × 3a–3 2a+2 ÷ a 2 +a a 2 +a+2 = a+1 a–1 × 3a–3 2a+2 × a 2 +a+2 a 2 +a = a+1 a–1 × 3 ( a–1 ) 2 ( a+1 ) × a 2 +a+2 a( a+1 ) = 3( a 2 +a+2 ) 2a( a+1 )
4. 64 a 2 –81 b 2 x 2 –81 × ( x–9 ) 2 8a–9b ÷ 8 a 2 +9ab ( x+9 ) 2 = 64 a 2 –81 b 2 x 2 –81 × ( x–9 ) 2 8a–9b ÷ ( x+9 ) 2 8 a 2 +9ab = ( 8a+9b ) ( 8a–9b ) ( x+9 ) ( x–9 ) × ( x–9 ) 2 8a–9b × ( x+9 ) 2 a ( 8a+9b ) = x 2 –81 a
5. x 2 –x–12 x 2 –49 × x 2 –x–56 x 2 +x–20 ÷ x 2 –5x–24 x+5 = x 2 –x–12 x 2 –49 × x 2 –x–56 x 2 +x–20 × x+5 x 2 –5x–24 = ( x–4 ) ( x+3 ) ( x–7 ) ( x+7 ) × ( x–8 ) ( x+7 ) ( x+5 ) ( x–4 ) × x+5 ( x–8 ) ( x+3 ) = 1 x–7
6. a 2 –8a+7 a 2 –11a+30 × a 2 –36 a 2 –1 ÷ a 2 –a–42 a 2 –4a–5 = a 2 –8a+7 a 2 –11a+30 × a 2 –36 a 2 –1 × a 2 –4a–5 a 2 –a–42 = ( a–7 ) ( a–1 ) ( a–6 ) ( a–5 ) × ( a+6 ) ( a–6 ) ( a+1 ) ( a–1 ) × ( a–5 ) ( a+1 ) ( a–7 ) ( a+6 ) =1
7. x 4 –27x x 2 +7x–30 × x 2 +20x+100 x 3 +3 x 2 +9x ÷ x 2 –100 x–3 = x 4 –27x x 2 +7x–30 × x 2 +20x+100 x 3 +3 x 2 +9x × x–3 x 2 –100 = x ( x 3 –27 ) ( x+10 ) ( x–3 ) × ( x+10 ) 2 x ( x 2 +3x+9 ) × x–3 ( x–10 ) ( x+10 ) = ( x–3 ) ( x 2 +3x+9 ) ( x–10 ) ( x 2 +3x+9 ) = x–3 x–10
8. a 2 +1 3a–6 ÷ ( a 3 +a 6a–12 × 4x+8 x–3 ) = a 2 +1 3( a–2 ) ÷ [ a( a 2 +1 ) ( a–2 ) × ( x+2 ) x–3 ] = a 2 +1 3( a–2 ) ÷ 2a( a 2 +1 ) ( x+2 ) 3( a–2 ) ( x–3 ) = a 2 +1 3 ( a–2 ) × 3 ( a–2 ) ( x–3 ) 2a ( a 2 +1 ) ( x+2 ) = x–3 2a( x+2 )
9. 8 x 2 –10x–3 6 x 2 +13x+6 × 4 x 2 –9 3 x 2 +2x ÷ 8 x 2 +14x+3 9 x 2 +12x+4 = 8 x 2 –10x–3 6 x 2 +13x+6 × 4 x 2 –9 3 x 2 +2x × 9 x 2 +12x+4 8 x 2 +14x+3 = 8 x 2 +2x–12x–3 6 x 2 +9x+4x+6 × ( 2x–3 ) ( 2x+3 ) x ( 3x+2 ) × ( 3x+2 ) 2 8 x 2 +2x+12x+3 = 2x( 4x+1 ) –3( 4x+1 ) 3x( 2x+3 ) +2( 2x+3 ) × ( 2x–3 ) ( 2x+3 ) x × ( 3x+2 ) 2x( 4x+1 ) +3( 4x+1 ) = ( 2x–3 ) ( 4x+1 ) ( 3x+2 ) ( 2x+3 ) × ( 2x–3 ) ( 2x+3 ) x × ( 3x+2 ) ( 2x+3 ) ( 4x+1 ) = ( 2x–3 ) 2 x( 2x+3 )
10. ( a+b ) 2 – c 2 ( a–b ) 2 – c 2 × ( a+c ) 2 – b 2 a 2 +ab–ac ÷ a+b+c a 2 = ( a+b ) 2 – c 2 ( a–b ) 2 – c 2 × ( a+c ) 2 – b 2 a 2 +ab–ac × a 2 a+b+c = [ ( a+b ) +c ] [ ( a+b ) –c ] [ ( a–b ) –c ] [ ( a–b ) +c ] × [ ( a+c ) +b ] [ ( a+c ) –b ] a ( a+b+c ) × a 2 a+b+c = ( a+b+c ) ( a+b–c ) ( a–b–c ) ( a–b+c ) × ( a+b+c ) ( a–b+c ) a+b+c × a a+b+c = a( a+b–c ) a–b–c
11. a 2 –5a b+ b 2 ÷ ( a 2 +6a–55 b 2 –1 × ax+3a a b 2 +11 b 2 ) = a( a–5 ) b( 1+b ) ÷ [ ( a+11 ) ( a–5 ) ( b+1 ) ( b–1 ) × a( x+3 ) b 2 ( a+11 ) ] = a( a–5 ) b( 1+b ) ÷ [ a( x+3 ) ( a–5 ) b 2 ( b+1 ) ( b–1 ) ] = a ( a–5 ) b ( 1+b ) × b 2 ( b+1 ) ( b–1 ) a ( x+3 ) ( a–5 ) = b( b–1 ) x+3
12. m 3 +6 m 2 n+9m n 2 2 m 2 n+7m n 2 +3 n 3 × 4 m 2 – n 2 8 m 2 –2mn– n 2 ÷ m 3 +27 n 3 16 m 2 +8mn+ n 2 = m 3 +6 m 2 n+9m n 2 2 m 2 n+7m n 2 +3 n 3 × 4 m 2 – n 2 8 m 2 –2mn– n 2 × 16 m 2 +8mn+ n 2 m 3 +27 n 3 = m( m 2 +6mn+9 n 2 ) n( 2 m 2 +7mn+3 n 2 ) × ( 2m–n ) ( 2m+n ) 8 m 2 –4mn+2mn– n 2 × ( 4m+n ) 2 ( m+3n ) ( m 2 –3mn+9 n 2 ) = m ( m+3n ) 2 n( 2 m 2 +mn+6mn+3 n 2 ) × ( 2m–n ) ( 2m+n ) 4m( 2m–n ) +n( 2m–n ) × ( 4m+n ) 2 ( m+3n ) ( m 2 –3mn+9 n 2 ) = m( m+3n ) n[ m( 2m+n ) +3n( 2m+n ) ] × ( 2m–n ) ( 2m+n ) ( 4m+n ) ( 2m–n ) × ( 4m+n ) 2 m 2 –3mn+9 n 2 = m ( m+3n ) n ( m+3n ) ( 2m+n ) × 2m+n × 4m+n m 2 –3mn+9 n 2 = m( 4m+n ) n( m 2 –3mn+9 n 2 )
13. ( a 2 –ax ) 2 a 2 + x 2 × 1 a 3 + a 2 x ÷ ( a 3 – a 2 x a 2 +2ax+ x 2 × a 2 – x 2 a 3 +a x 2 ) = [ a( a–x ) ] 2 a 2 + x 2 × 1 a 2 ( a+x ) ÷ [ a 2 ( a–x ) ( a+x ) 2 × ( a–x ) ( a+x ) a ( a 2 + x 2 ) ] = a 2 ( a–x ) 2 a 2 + x 2 × 1 a 2 ( a+x ) ÷ a ( a–x ) 2 ( a+x ) ( a 2 + x 2 ) = ( a–x ) 2 a 2 + x 2 × 1 ( a+x ) × ( a+x ) ( a 2 + x 2 ) a ( a–x ) 2 = 1 a
14. ( a 2 –3a ) 2 9– a 2 × 27– a 3 ( a+3 ) 2 –3a ÷ a 4 –9 a 2 ( a 2 +3a ) 2 = ( a 2 –3a ) 2 9– a 2 × 27– a 3 ( a+3 ) 2 –3a × ( a 2 +3a ) 2 a 4 –9 a 2 = [ a( a–3 ) ] 2 ( 3–a ) ( 3+a ) × ( 3–a ) ( 9+3a+ a 2 ) a 2 +6a+9–3a × [ a( a+3 ) ] 2 a 2 ( a 2 –9 ) = a 2 ( a–3 ) 2 3+a × 9+3a+ a 2 a 2 +3a+9 × a 2 ( a+3 ) 2 a 2 ( a–3 ) ( a+3 ) = a 2 ( a–3 )