(3-(9x-1)/(x+3x^2))*(x+1+(4)/(9x-3))

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Solution for (3-(9x-1)/(x+3x^2))*(x+1+(4)/(9x-3)) equation: 


D( x )

3*x^2+x = 0

9*x-3 = 0

3*x^2+x = 0

3*x^2+x = 0

3*x^2+x = 0

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

DELTA = 1

DELTA > 0

x = (1^(1/2)-1)/(2*3) or x = (-1^(1/2)-1)/(2*3)

x = 0 or x = -1/3

9*x-3 = 0

9*x-3 = 0

9*x-3 = 0 // + 3

9*x = 3 // : 9

x = 3/9

x = 1/3

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

(3-((9*x-1)/(3*x^2+x)))*(4/(9*x-3)+x+1) = 0

((-1*(9*x-1))/(3*x^2+x)+3)*(4/(9*x-3)+x+1) = 0

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

3*x^2+x = 0

3*x^2+x = 0

x*(3*x+1) = 0

3*x+1 = 0 // - 1

3*x = -1 // : 3

x = -1/3

x*(x+1/3) = 0

(-1*(9*x-1))/(x*(x+1/3))+3 = 0

(-1*(9*x-1))/(x*(x+1/3))+(3*x*(x+1/3))/(x*(x+1/3)) = 0

3*x*(x+1/3)-1*(9*x-1) = 0

3*x^2-8*x+1 = 0

3*x^2-8*x+1 = 0

3*x^2-8*x+1 = 0

DELTA = (-8)^2-(1*3*4)

DELTA = 52

DELTA > 0

x = (52^(1/2)+8)/(2*3) or x = (8-52^(1/2))/(2*3)

x = (2*13^(1/2)+8)/6 or x = (8-2*13^(1/2))/6

(x-((8-2*13^(1/2))/6))*(x-((2*13^(1/2)+8)/6)) = 0

((x-((8-2*13^(1/2))/6))*(x-((2*13^(1/2)+8)/6)))/(x*(x+1/3)) = 0

((x-((8-2*13^(1/2))/6))*(x-((2*13^(1/2)+8)/6)))/(x*(x+1/3)) = 0 // * x*(x+1/3)

(x-((8-2*13^(1/2))/6))*(x-((2*13^(1/2)+8)/6)) = 0

4/(9*x-3)+x+1 = 0

4/(9*x-3)+(x*(9*x-3))/(9*x-3)+(1*(9*x-3))/(9*x-3) = 0

x*(9*x-3)+1*(9*x-3)+4 = 0

9*x^2-3*x+9*x-3+4 = 0

9*x^2+6*x+1 = 0

9*x^2+6*x+1 = 0

9*x^2+6*x+1 = 0

DELTA = 6^2-(1*4*9)

DELTA = 0

x = -6/(2*9)

x = -1/3 or x = -1/3

(x+1/3)^2 = 0

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

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

(x+1/3)^2 = 0

(x-((8-2*13^(1/2))/6))*(x-((2*13^(1/2)+8)/6))*(x+1/3)^2 = 0

( x+1/3 )

x+1/3 = 0 // - 1/3

x = -1/3

( x-((2*13^(1/2)+8)/6) )

x-((2*13^(1/2)+8)/6) = 0 // + (2*13^(1/2)+8)/6

x = (2*13^(1/2)+8)/6

( x-((8-2*13^(1/2))/6) )

x-((8-2*13^(1/2))/6) = 0 // + (8-2*13^(1/2))/6

x = (8-2*13^(1/2))/6

x in { -1/3} 

x in { (2*13^(1/2)+8)/6, (8-2*13^(1/2))/6 }

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