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Esercizi svolti sulle espressioni letterali e le frazioni algebriche.

1. $x/(bx+b-x-1) – x/(bx+b+x+1) – 2/(b^2 -1)$

2. $(4/(x^2-4) – (x-2)/(x+2))(1-6/(4-x))(1-2/x)$

3. 10 semplificazioni di frazioni algebriche

4. $-[-(-3/2x^2y^2)(3/2xyz)+(-1/3x^4y^4z):(5/6xy)]((10)/(37)xz)-…$

5. $[(-3/2a^2b)^5:(-3/2a^2b)^3-(3/2a^2b)^2(-4ab^3):(-2ab^3)]^2:(-1/2ab^2)^2+…$

6. $-2(x^2y^4)^3:[(4x^3)^2(-1/2y^3)^4]+[-5/3a^2+4/3a^2b^2:(-2/3b)^2]^2:(-2a)^4$

7. $[(x^4y^2)(-x^5y^4)]:[(-x^2y)(x^2y^3)]-(3/2xy):(-3/2xy)+3(-x^2y)(x^3y)$

8. $2ab^2-[1/3ab+3ab^2+(a^2b^2-4a^2b^2):(ab)-1/3ab]-3a(-b^2)+ab-2ab^2$

9. $(-(82)/(21)a^4b^5c):(-5/(21)a^2b^2c)-(-2/7a^5b^7):(-5/7a^3b^4)$

10. $(-4x^6y^3t^4):(2x^4y^3t^2)+(-14x^5y^2t^3):(-7x^3y^2t)$

11. $(1/5x^2y)(-(25)/4x^2y^4):(-7/4xy^2)$

12. $(-3/4a^4b^2):(1/4ab)-3a^3b(1/3b^2)+a^3(2+b^3)$

13. $3x^3y-[-(x+2x)(3/2x)(-1/3xy)+2x(xy)(-1/2x)]-[-5x(-xy)(-x)]$

14. $-6x^3bt(-4xb^3t)-(-2bt^2)(-7x^4b^3)+5b(-2x^4b^3t^2)$

15. $(1/6xy+1/3xy-3/2xy)[xy+x(2x)-2x^2]+3x(xy^2)$

16. $2a^2+[-(-3/4ab)(-a)+(-1/6a)(3/2ab)](-1/2ab+3ab)-(1/3a)(a^2b^2)+2a(-a)$

17. $1/4-(-3abc)(-1/9a^2b)+(-1/3)(-9/2)+(1/4a)(-8/3a^2b^2c)$

18. $3x^2y^2+2xy^2(-3/2x)+xy(-3xy)-(-2x)(1/2xy^2)$

19. $3/5x^2y((15)/2xy^3)+(-3/4xy)(-2/9x^2y)(3/2y^2)$

20. $-1/2x(-4x^3)-(-3x^2)(1/3x^2)$

21. Calcolare $1/2x+3x+(-2x)+4x-(3/2x+4x)$ per$x=-1$

22. Calcolare $3a+(-5a)+(-7a)+4a+(-a)$ per $a=2$

23. $3x^2y+[-(-4x^2y)+(-5x^2y)+(7x^2y-3x^2y)]+x^2y$

24. $3/2x+4+(2/7xy)+3+(-8/7xy)-2+5/(14)xy-xy$

25. $(xy-2)(xy+2)-7x^2+14y^2-x^2y^2-17$

26. $3x^2(x+1)-6(x^3+x^2-1/2x)+3x(x^2-1)$

27. $-9x^4-20y^4+12x^2y^2$

28. $(1/2x^2-3y)^2-(x^2-1/2y)^2-7y(5/4y-2/7x^2)$

29. $(x^2+2y^2)^2-(3x^2-4y^2)(3x^2+4y^2)-(3xy)^2$

30. $(a-b)(a+b)-(3a-b)(3a+b)$

31. $(x+1)^2+x(x+1)-2(x-1)^2$

32. $(a+2)(a+5)-(21a^2+30a):(3a)$

33. $(3x^4-2x^2+x^3):x^2-(3x+1)x$

34. $(4a^2b^3-3ab):a+(3b^2-2ab^4):b$

35. $[(x^2-1/2xy)(2x^2+xy)-1/2(2x^2)^2]^2:(-3/4xy^2)+x^3(1/3y-x)(3x+y)$

36. $(2m^(p+2)-6m^(p+1)):(2m^p)$

37. $(4x-2/3y)(3/2y+1/4x)-(x+y)(x-y)$

38. $(y+2x)(1/2y-x+1)-(1/2y+x)(y-2x)$

39. $(x-1)(x+2)-(x+5)(x-4)+3(x+1)$

40. $x^2(x-y)+y^2(x-y)-(x^2+y^2)(x-y)$

41. $-(3/2xy)^2+2/3x^2y(y+9/4x^2y^3)+(38)/(24)x^2y^2$

42. $x(2x-y)+3y(5x+4)-2y(5x+3y)$

43. $a(2a-2)+2a(3-a)-a(5b-2)$

44. $x(2x+1)+x(3x-1)$

45. $(1/2xy^3-2xy^3)^2:(13x^2y^4-4x^2y^4)+(1/2y^2-4/5y^2)^2:(-1/10y^2)$

46. $(a^2/(4a^2+4ab+b^2)-(a-b)/(6a+3b)):(a^3-b^3)/(12a+6b)$

47. $(b+2)/(b-2)-(b+1)/(b-1)-2/(b^2-3b+2)$

48. $[2a^4-(a^2+b+1)(a^2-b-1)][a^4-(b+1)^2]+(b+1)^4$

49. $(a-b)/(a+b)-…/(a^2+2ab+b^2)=(a-3b)/(a+b)$

50. $(frac{a^2}{4a^2+4ab+b^2} – frac{a-b}{6a+3b}):(frac{a^3-b^3}{12a+6b])$