Ejercicio 122

Ejercicio 122

1. 3 2a = 4 a 2 4 a 2 ÷ 2a =2a 3 × 2a =6a 6a 4 a 2
2. 5 9 x 2 = 20a 20a ÷ 5 =4a 9 x 2 × 4a =36a x 2 20a 36a x 2
3. m a b 2 = 2 a 2 b 2 2 a 2 b 2 ÷ a b 2 =2a m × 2a =2am 2am 2 a 2 b 2
4. 3x 8y = 9 x 2 y 2 9 x 2 y 2 ÷ 3x =3x y 2 8y × 3x y 2 =24x y 3 9 x 2 y 2 24x y 3
5. 4m 5 n 2 = 5 n 3 5 n 3 ÷ 5 n 2 =n 4m × n =4mn 4mn 5 n 3
6. 2x+7 5 = 15 15 ÷ 5 =3 3( 2x+7 ) =6x+21 6x+21 15
7. 2x x–1 = x 2 –x x 2 –x ÷ x–1 =x( x–1 ) ÷ x–1 =x x × 2x =2 x 2 2 x 2 x 2 –x
8. a 2 a+2 = 2 a 3 2 a 3 ÷ a 2 =2a 2a( a+2 ) =2 a 2 +4a 2 a 3 2 a 2 +4a
9. 3a a+b = a 2 +2ab+ b 2 a 2 +2ab+ b 2 ÷ a+b = ( a+b ) 2 ÷ a+b =a+b 3a( a+b ) =3 a 2 +3ab 3 a 2 +3ab a 2 +2ab+ b 2
10. x–4 x+3 = x 2 +5x+6 x 2 +5x+6 ÷ x+3 =( x+3 ) ( x+2 ) ÷ x+3 =x+2 ( x+2 ) ( x–4 ) = x 2 –2x–8 x 2 –2x–8 x 2 +5x+6
11. 2a x+a = 2 a 3 2 a 3 ÷ 2a = a 2 a 2 ( x+a ) = a 2 x+ a 3 2 a 3 a 2 x+ a 3
12. x–y 6 = 12 12 ÷ 6 =2 2( x–y ) =2x–2y 2x–2y 12
13. 5x a–b = a 2 – b 2 a 2 – b 2 ÷ a–b =( a–b ) ( a+b ) ÷ a–b =a+b 5x( a+b ) =5ax+5bx 5ax+5bx a 2 – b 2
14. x–5 a = 3 x 2 –15x 3 x 2 –15x ÷ x–5 =3x( x–5 ) ÷ x–5 =3x a × 3x =3ax 3 x 2 –15x 3ax
15. 5x 2x+y = 4 x 2 +4xy+ y 2 4 x 2 +4xy+ y 2 ÷ 2x+y = ( 2x+y ) 2 ÷ 2x+y =2x+y 5x( 2x+y ) =10 x 2 +5xy 10 x 2 +5xy 4 x 2 +4xy+ y 2
16. x+3 x+1 = x 2 –9 x 2 –9 ÷ x+3 =( x+3 ) ( x–3 ) ÷ x+3 =x–3 ( x+1 ) ( x–3 ) = x 2 –2x–3 x 2 –9 x 2 –2x–3
17. 2 a+1 = a 3 +1 a 3 +1 ÷ a+1 =( a+1 ) ( a 2 –a+1 ) ÷ a+1 = a 2 –a+1 2( a 2 –a+1 ) =2 a 2 –2a+2 2 a 2 –2a+2 a 3 +1
18. x–2y 3x = 9 x 2 y 9 x 2 y ÷ 3x =3xy 3xy( x–2y ) =3 x 2 y–6xy 3 x 2 y–6x y 2 9 x 2 y
19. x–1 x+1 = x 2 –1 x 2 –1 ÷ x–1 =( x–1 ) ( x+1 ) ÷ x–1 =x+1 ( x+1 ) ( x+1 ) = ( x+1 ) 2 x 2 –1 ( x+1 ) 2
20. a–b 7 a 2 = 63 a 3 b 63 a 3 b ÷ 7 a 2 =9ab 9ab( a–b ) =9 a 2 b–9a b 2 9 a 2 b–9a b 2 63 a 3 b
21. x+1 x+5 = x 2 +3x–10 x 2 +3x–10 ÷ x+5 =( x+5 ) ( x–2 ) ÷ x+5 =x–2 ( x+1 ) ( x–2 ) = x 2 –x–2 x 2 –x–2 x 2 +3x–10