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Amplificarea, simplificarea rapoartelor algebrice (Exerciții aplicative)
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Începe jocul
Aplicația este accesibilă de pe ecrane late
Amplificați cu x, apoi cu (x-1) următoarele rapoarte:
(x^2-x-1)/(x+2) =
Amplificat cu x:
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^3-x^2-x)/(x^2+2x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^3-4x^2+4x-1)/(x^3-1)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(x^3-3x^2+x)/(x^3+x^2+x)
(2x^3+x^2-3x)/(x^2+3x)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(x^3-2x^2+1)/(x^2+x-2)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
;
Amplificat cu (x-1):
(x^3-3x^2+x)/(x^3+x^2+x)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(x^3-2x^2+1)/(x^2+x-2)
(x^3-x^2-x)/(x^2+2x)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^3-4x^2+4x-1)/(x^3-1)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(2x^3+x^2-3x)/(x^2+3x)
;
(2x^2+x-3)/(x+3) =
Amplificat cu x:
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^3-x^2-x)/(x^2+2x)
(x^3-4x^2+4x-1)/(x^3-1)
(x^3-2x^2+1)/(x^2+x-2)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(x^3-3x^2+x)/(x^3+x^2+x)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(2x^3+x^2-3x)/(x^2+3x)
(x^3-2x^2-2x)/(2x^3-x^2-x)
;
Amplificat cu (x-1):
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(x^3-3x^2+x)/(x^3+x^2+x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^3-2x^2+1)/(x^2+x-2)
(x^3-4x^2+4x-1)/(x^3-1)
(2x^3+x^2-3x)/(x^2+3x)
(x^3-x^2-x)/(x^2+2x)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^3-2x^2-2x)/(2x^3-x^2-x)
;
(x^2-3x+1)/(x^2+x+1) =
Amplificat cu x:
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(x^3-2x^2+1)/(x^2+x-2)
(x^3-3x^2+x)/(x^3+x^2+x)
(2x^3+x^2-3x)/(x^2+3x)
(x^3-x^2-x)/(x^2+2x)
(x^3-4x^2+4x-1)/(x^3-1)
;
Amplificat cu (x-1):
(x^3-2x^2+1)/(x^2+x-2)
(x^3-4x^2+4x-1)/(x^3-1)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(x^3-3x^2+x)/(x^3+x^2+x)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(2x^3+x^2-3x)/(x^2+3x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(x^3-x^2-x)/(x^2+2x)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
;
(x^2-2x-2)/(2x^2-x-1) =
Amplificat cu x:
(x^3-3x^2+x)/(x^3+x^2+x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^3-x^2-x)/(x^2+2x)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(2x^3+x^2-3x)/(x^2+3x)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(x^3-4x^2+4x-1)/(x^3-1)
(x^3-2x^2+1)/(x^2+x-2)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
;
Amplificat cu (x-1):
(x^3-2x^2+1)/(x^2+x-2)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(x^3-3x^2+x)/(x^3+x^2+x)
(x^3-4x^2+4x-1)/(x^3-1)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(2x^3+x^2-3x)/(x^2+3x)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^3-x^2-x)/(x^2+2x)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
;
(3x^2-2x-1)/(x^2+2x+3) =
Amplificat cu x:
(x^3-3x^2+2)/(2x^3-3x^2+1)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(x^3-3x^2+x)/(x^3+x^2+x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(x^3-4x^2+4x-1)/(x^3-1)
(x^3-x^2-x)/(x^2+2x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^3-2x^2+1)/(x^2+x-2)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(2x^3+x^2-3x)/(x^2+3x)
;
Amplificat cu (x-1):
(x^3-3x^2+x)/(x^3+x^2+x)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(x^3-4x^2+4x-1)/(x^3-1)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(x^3-x^2-x)/(x^2+2x)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^3-2x^2+1)/(x^2+x-2)
(2x^3+x^2-3x)/(x^2+3x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
;
(x^3-2x^2-x-1)/(x^2+3x-1) =
Amplificat cu x:
(x^3-2x^2-2x)/(2x^3-x^2-x)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^3-2x^2+1)/(x^2+x-2)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(x^3-3x^2+2)/(2x^3-3x^2+1)
(2x^3+x^2-3x)/(x^2+3x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^3-3x^2+x)/(x^3+x^2+x)
(x^3-x^2-x)/(x^2+2x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(x^3-4x^2+4x-1)/(x^3-1)
;
Amplificat cu (x-1):
(x^3-x^2-x)/(x^2+2x)
(2x^3-x^2-4x+3)/(x^2+2x-3)
(x^3-2x^2-2x)/(2x^3-x^2-x)
(3x^3-5x^2+x+1)/(x^3+x^2+x-3)
(x^3-2x^2+1)/(x^2+x-2)
(x^4-2x^3-x^2-x)/(x^3+3x^2-x)
(x^3-3x^2+x)/(x^3+x^2+x)
(3x^3-2x^2-x)/(x^3+2x^2+3x)
(2x^3+x^2-3x)/(x^2+3x)
(x^3-4x^2+4x-1)/(x^3-1)
(x^4-3x^3+x^2+1)/(x^3+2x^2-4x+1)
(x^3-3x^2+2)/(2x^3-3x^2+1)
;
