1. Wykonaj działanie : 2/(x^3+8)-1/(x+2)+5/(x^2-2x+4)
2. Rozwiąż równanie :(6-x)/(x-7)=9-3x+1/(x-7)

2/(x^3+8)-1/(x+2)+5/(x^2-2x+4)= 2/(x+2)(x^2-2x+4)- 1/(x+2)+5/(x^2-2x+4)= 2/(x+2)(x^2+2x+4)-(x^2-2x+4)/(x+2)(x^2-2x+4)+(5x+10)/(x+2)(x^2-2x+4)= (2-x^2+2x-4+5x+10/(x+2)(x^2-2x+4)= (-x^2+7x+8)/(x+2)(x^2-2x+4)

2)

(6-x)/(x-7)=9-3x+1/(x-7)
6-x/(x-7)=(9-3x)(x-7)/(x-7)+1/(x-7)
(6-x)-(9-3x)(x-7)-1/(x-7)=0
(6-x-9x-3x^2+63-21x-1)/(x-7)=0
(3x^2-11x+68)/(x-7)=0

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SmokRozanyviz SmokRozanyviz · Answer 2

1)
2/(x^3 + 8) – 1/(x + 2) + 5/(x^2 - 2x + 4) = 2/(x + 2)(x^2 - 2x + 4) – 1/(x + 2) + 5/(x^2 -2x + 4) = 2/(x + 2)(x^2 - 2x + 4) – (x^2 - 2x + 4)/(x + 2)(x^2 - 2x + 4) + 5(x + 2)/(x + 2)(x^2 -2x + 4) = [2 – (x^2 - 2x + 4) + 5x + 10]/(x + 2)(x^2 - 2x + 4) = (2 – x^2 + 2x – 4 + 5x + 10) )/(x + 2)(x^2 - 2x + 4) = (-x^2 + 7x + 8) )/(x + 2)(x^2 - 2x + 4)

2)
(6 – x)/(x – 7) = 9 – 3x + 1/(x – 7) /*(x – 7)
6 – x = (9 – 3x)(x – 7) + 1
6 – x = 9x – 63 – 3x^2 + 21x + 1
6 – x = -3x^2 + 30x – 62
0 = -3x^2 + 31x – 68
3x^2 - 31x + 68 = 0
Δ = 31^2 – 4 * 3 * 68
Δ = 961 – 816
Δ = 145
x1 = (31 - √145)/6
x2 = (31 + √145)/6

Czakuviz Czakuviz · Answer 3

Czakuviz Czakuviz

(6-x)/(x-7)=9-3x+1/(x-7)
(6-x)=9-3x+1 licznik
(x-7) = (x-7) mianownik
(6-x)(x-7)=(x-7)(9-3x+1)
6x-42-x2+7x=9x-3x2+x-63+21x-7
2x2-18x+28=
/:2
x2-9x+14=0
delta=b2-4ac=81-56
pierwiastek z delty=5
x1=-b+pierwiastek z delty licznik
2a mianownik
czyli 9+5 licznik
2 mianownik
czyli x1=7
x2=-b + pierwiastek z delty - licznik
2a - mianownik
czyli x2=2

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