(9-k^-2)/(3k^-1-k^-2)

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Solution for (9-k^-2)/(3k^-1-k^-2) equation:


D( k )

3*k^-1-k^-2 = 0

k = 0

3*k^-1-k^-2 = 0

3*k^-1-k^-2 = 0

t_1 = k^-1

3*t_1^1-1*t_1^2 = 0

3*t_1-t_1^2 = 0

DELTA = 3^2-(-1*0*4)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)-3)/(-1*2) or t_1 = (-9^(1/2)-3)/(-1*2)

t_1 = 0 or t_1 = 3

t_1 = 0

k^-1+0 = 0

k^-1 = 0

1*k^-1 = 0 // : 1

k^-1 = 0

k należy do O

t_1 = 3

k^-1-3 = 0

1*k^-1 = 3 // : 1

k^-1 = 3

-1 < 0

1/(k^1) = 3 // * k^1

1 = 3*k^1 // : 3

1/3 = k^1

k = 1/3

k = 0

k = 0

k in (-oo:0) U (0:1/3) U (1/3:+oo)

(9-k^-2)/(3*k^-1-k^-2) = 0

3*k^-1-k^-2 = 0

k^-1*(3-k^-1) = 0

-1*k^-1 = -3 // : -1

k^-1 = 3

-1 < 0

1/(k^1) = 3 // * k^1

1 = 3*k^1 // : 3

1/3 = k^1

k = 1/3

k^-1*(k-1/3) = 0

(9-k^-2)/(k^-1*(k-1/3)) = 0

-1*k^-2 = -9 // : -1

k^-2 = 9

-2 < 0

1/(k^2) = 9 // * k^2

1 = 9*k^2 // : 9

1/9 = k^2

k^2 = 1/9 // ^ 1/2

abs(k) = 1/3

k = 1/3 or k = -1/3

k in { 1/3}

k = -1/3

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