-2/(3n-3)+3/(3n+3)=-1/(9n^2-9)

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Solution for -2/(3n-3)+3/(3n+3)=-1/(9n^2-9) equation:


D( n )

3*n-3 = 0

3*n+3 = 0

9*n^2-9 = 0

3*n-3 = 0

3*n-3 = 0

3*n-3 = 0 // + 3

3*n = 3 // : 3

n = 3/3

n = 1

3*n+3 = 0

3*n+3 = 0

3*n+3 = 0 // - 3

3*n = -3 // : 3

n = -3/3

n = -1

9*n^2-9 = 0

9*n^2-9 = 0

9*n^2 = 9 // : 9

n^2 = 1

n^2 = 1 // ^ 1/2

abs(n) = 1

n = 1 or n = -1

n in (-oo:-1) U (-1:1) U (1:+oo)

3/(3*n+3)-2/(3*n-3) = -1/(9*n^2-9) // + -1/(9*n^2-9)

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

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

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

(-2*(3*n+3)*(9*n^2-9))/((3*n-3)*(3*n+3)*(9*n^2-9))+(3*(3*n-3)*(9*n^2-9))/((3*n-3)*(3*n+3)*(9*n^2-9))+((3*n-3)*(3*n+3))/((3*n-3)*(3*n+3)*(9*n^2-9)) = 0

3*(3*n-3)*(9*n^2-9)-2*(3*n+3)*(9*n^2-9)+(3*n-3)*(3*n+3) = 0

27*n^3-135*n^2+9*n^2-27*n-9+135 = 0

27*n^3-126*n^2-27*n+126 = 0

27*n^3-126*n^2-27*n+126 = 0

9*(3*n^3-14*n^2-3*n+14) = 0

3*n^3-14*n^2-3*n+14 = 0

{ 1, -1, 2, -2, 7, -7, 14, -14 }

1

n = 1

3*n^3-14*n^2-3*n+14 = 0

1

n-1

3*n^2-11*n-14

3*n^3-14*n^2-3*n+14

n-1

3*n^2-3*n^3

14-11*n^2-3*n

11*n^2-11*n

14-14*n

14*n-14

0

3*n^2-11*n-14 = 0

DELTA = (-11)^2-(-14*3*4)

DELTA = 289

DELTA > 0

n = (289^(1/2)+11)/(2*3) or n = (11-289^(1/2))/(2*3)

n = 14/3 or n = -1

n in { -1, 14/3, 1}

9*(n+1)*(n-14/3)*(n-1) = 0

(9*(n+1)*(n-14/3)*(n-1))/((3*n-3)*(3*n+3)*(9*n^2-9)) = 0

(9*(n+1)*(n-14/3)*(n-1))/((3*n-3)*(3*n+3)*(9*n^2-9)) = 0 // * (3*n-3)*(3*n+3)*(9*n^2-9)

9*(n+1)*(n-14/3)*(n-1) = 0

( n+1 )

n+1 = 0 // - 1

n = -1

( n-1 )

n-1 = 0 // + 1

n = 1

( n-14/3 )

n-14/3 = 0 // + 14/3

n = 14/3

n in { -1}

n in { 1}

n = 14/3

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