Home ▸ Esercizi svolti ▸ Espressioni letterali

Esercizi svolti sulle espressioni letterali e le frazioni algebriche.

1. Determinare il valore della seguente espressione letterale : $ [(-1/3 a^2)^2 – (1 + 2a) – (-a)^2 ] – (1/9 a^4 – a^2 – 3) – (-2)^2 $

2. Semplificare la seguente espressione letterale: $ (- a^(2n))^2 + (a^(3n))^2 – (a^6)^n + a^(4n)$

3. Semplificare la seguente espressione letterale: $ (3/4 a b^2 x^4 y^2) : (- 1/3 a b x^4) $

4. Risolvere la seguente espressione: $ 3/5 a x^3 – (+ 1/3 a^3 x) + 3/2 x^3 a – 5/3 x a^3 – (- 1/2 a^3 x) $

5. $$ \left( \sqrt[3]{2 \sqrt[3]{2 \sqrt{\frac{1}{2}}}} · \sqrt[3]{\frac{1}{2} \sqrt[3]{2 \sqrt[3]{\frac{1}{4}}}} \right)^6 · \sqrt[3]{4 \sqrt{2}} $$

6. Semplifica la seguente espressione letterale: $$ \left( \sqrt{a \sqrt[3]{a}} : \sqrt[3]{a \sqrt[3]{a}}+ \sqrt[9]{a^2} + \frac{\sqrt[6]{a^5}}{\sqrt[9]{a}} : \sqrt{a} \right) · \frac{\sqrt[9]{a}}{3}  $$

7. $ (frac(a)(a – b) – frac(b)(a + b) + frac(a^2 + b^2)(a^2 – b^2)) : (a – b + frac(a^2 + 3b^2)(a + b))$

8. $ ( 1 – frac( x + 1)(x – 1)) : frac(x – 2)(x – 1) + frac(3x + 6)(x^2 – 4) – frac(2)(x^2 – 3x + 2) : (frac(x)(x + 3) – frac(x)(x – 3)) + frac(2x – 2)(x(x – 2)(x – 1)^2) $

9. $ frac(x^2 + 2x + 1)(1 – x^2) – frac(x^3 – 1)( x – 1) + frac(2 – 8x)(4x – 1) $

10. $ frac(x^2 – 4x + 4)(x^3 – 8) * frac(x^2 + 2x + 4)(x^2 – 2x) $

11. $ frac(6a^2b^3 – 9a^3b^2)(2ab – 3a^2 – 2b + 3a)$

12. ${[(frac(4)(x – 2) + frac(1)(1 – x) – frac(5x – 4)(x^2 – 3x + 2)) : frac(2x – 3)(x^2 – 5x + 6)] : (x^2 – 2x – 3) – frac(x)(3 – 2x) } * frac(x + 1)(x – 1)$

13. Semplifica la seguente espressione letterale: $ frac(a)(x + 1) + frac(a + b)(x^2 – 1) – frac(b)(x – 1) $

14. Semplifica la seguente espressione letterale: $ frac(2x)(x + 3) – frac(3x – 1)(2x + 6) + frac(3)(3x + 9) $

15. Scomponi e semplifica: $ frac(ax + a – x – 1)(ax – a – 2x + 2) * frac(ax – 2a – 2x + 4)(x^2 – x – 2) $

16. Scomponi in fattori e semplifica: $ frac(4x^2 – xy – 4x + y)(1 – x^2)$

17. $(-5/2 a^3 b^2 x^4 y) : (- 4/5 a^2 b x^4 )$

18. $ 1/5 a^2 x – (- 1/2 a^2 x) – 1/2 a^2 x + 2/3 a^2 x – (3/4 a^2 x) $

19. $ 6(x – 2) + 5x – 5(x + 1) – 2(x – 3) + 5 = $

20. $ [(- 1/3 a^2 )^2 – (1 + 2a) – (-a)^2] – (1/9 a^4 – a^2 – 3) – (-2)^2 $

21. Calcola il valore del polinomio $x^4-2x^3+3x^2-2x+1$ per i seguenti valori della x….

22. $[4(x-1/2y)(x+1/2y)]^2-(2x-3y)^2(2x+3y)^2-16y^2(2x-y)(2x+y)+(-4y^2)^2$

23. $[(1/2ab-(1/4a+b)^2+(b+1/4a)(-1/4a+b)]a+(b+1/2a)^3-b^2(3/2a+b)$

24. $[(1/2x+2/3y+z)^2-(1/2+2/3y-z)^2+1/3yz]^2-3yz^2(4x+3y)$

25. $[(3ab)^3-(-5ab)^2xxab-(2+ab)^7:(8a^2b^2)^2]:(-3/4a^3b^2)^3$

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

27. ${[(-1/4a^2b^4)^2-(+1/2ab^2)^4-(-ab^2)^4]:(1/2a^2b)^2}^2:(2b)^3$

28. ${[-12/5a^2b^2xx(-25/6a^3b^3)]:(5ab)^2}:[2/5xx(ab)^6:a^3b^3]$

29. $[-x^3y^3+(1/2xy)^3-4x^2yxx(1/4xy^2)]:[5xx1/2xyxx(-xy)^2]$

30. $[2xy(-1/4x^2y)-(2x^2y)^3:(8x^3y)]:(1/4x^2+1/2x^2)$

31. $[(1/4ab^2)^3:(1/8a^2b^2]^2:[(1/2a^4b^3):(2/5a^2b)]$

32. $[(3/2a^3b)^2:(-3/4ab)]^2:(-2/3a^6b^2)+(5/2a^4-3a^3xx(-1/4a)$

33. $[3/4ab^3xx(-1/9a^2b^2)-(-3/2a^2b^3)^2:(+9/8ab)+2a^3b^5]:(-1/6a^2b^2)$

34. $(-3xz^2)(-4x^2z)(1/3x)-(-2/9x^2z)(-1/4z^2)(3x^2)+(-3/2x^4z^3)$

35. $(1/2ab^2)(-8/5a^2b)-2a^2b^2(-4ab)-2/5a(-5/3a^2)(+3b^3)$

36. $2ab-(1/3a^2b-1/9a^2b)+(3/2ab-2ab)+(-2/9a^2b+a^2b)-1/2ab+(-5/9a^2b)$

37. $9/7x^2zxx(-4/9x^2z^3+1/3x^2z^3-5/4x^2z^3)$

38. $(-3/10a^2b^2c^2)xx(-4/3a^2b^2+9/2a^2b^2-1/4a^2b^2)$

39. $2/5acxx(-5/6b^2c^2+3/2b^2c^2-b^2c^2)$

40. $3/4xyz^2-5/6x^3y-(-1/12x^3y)+xyz^2-(-1/4x^3y)-(+1/4xyz^2)+1/2x^3y$

41. $2a^3c+(-1/2a^3c)+(-1/2)-(+a^3c)-(-a^3c)+(-1/2a^rc)-(-1/2)$

42. $-(4/3)ab^3x-(-5/4ab^3x)+(-2ab^3x)-1/8ab^3x+1/12ab^3x$

43. $-3/2x^2y^4+(-4x^4y)+1/7x^2y^4-(-2x^4y)$

44. $-2ax-(-3a^2x)+(+1/3ax)-(-a^2x)$

45. $2xy+(-1/2a^2)+(-1/3xy)-(-2xy)$

46. $sqrt(a^2/5-1+4/(5a^2)):(sqrt(a-3+2/a)sqrt((a^2+a)/(5a+10)))=$

47. $(2/(a-2)-2/(a+3)-(5a)/(a^2+a-6))(1+3/a)^2=$

48. $(frac{a^2}{4a^2+b^2+4ab}-frac{a-b}{2a+b}+frac{a+b}{4a+2b}):(5/b + 3/a)$

49. $(1/(3x+1) +1/(3x-1)-1/(9x^2 -1)) : (2+ (6x)/(3x-1)) + 1/(6x+2)$

50. $(1-b/(a+b))(1+b/(a-b))(1-b^2 / a^2)$