(1/x)+(1/x-9)=(19)/(9x-33)

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Solution for (1/x)+(1/x-9)=(19)/(9x-33) equation: 


D( x )

x = 0

9*x-33 = 0

x = 0

x = 0

9*x-33 = 0

9*x-33 = 0

9*x-33 = 0 // + 33

9*x = 33 // : 9

x = 33/9

x = 11/3

x in (-oo:0) U (0:11/3) U (11/3:+oo)

1/x+1/x-9 = 19/(9*x-33) // - 19/(9*x-33)

1/x-(19/(9*x-33))+1/x-9 = 0

1/x-19*(9*x-33)^-1+1/x-9 = 0

1/x-19/(9*x-33)+1/x-9 = 0

(-19*x)/(x*(9*x-33))+(1*(9*x-33))/(x*(9*x-33))+(1*(9*x-33))/(x*(9*x-33))+(-9*x*(9*x-33))/(x*(9*x-33)) = 0

1*(9*x-33)+1*(9*x-33)-9*x*(9*x-33)-19*x = 0

9*x-81*x^2-10*x+297*x-33-33 = 0

297*x-81*x^2-x-66 = 0

296*x-81*x^2-66 = 0

296*x-81*x^2-66 = 0

296*x-81*x^2-66 = 0

DELTA = 296^2-(-81*(-66)*4)

DELTA = 66232

DELTA > 0

x = (66232^(1/2)-296)/(-81*2) or x = (-66232^(1/2)-296)/(-81*2)

x = (2*16558^(1/2)-296)/(-162) or x = (-2*16558^(1/2)-296)/(-162)

(x-((2*16558^(1/2)-296)/(-162)))*(x-((-2*16558^(1/2)-296)/(-162))) = 0

((x-((2*16558^(1/2)-296)/(-162)))*(x-((-2*16558^(1/2)-296)/(-162))))/(x*(9*x-33)) = 0

((x-((2*16558^(1/2)-296)/(-162)))*(x-((-2*16558^(1/2)-296)/(-162))))/(x*(9*x-33)) = 0 // * x*(9*x-33)

(x-((2*16558^(1/2)-296)/(-162)))*(x-((-2*16558^(1/2)-296)/(-162))) = 0

( x-((-2*16558^(1/2)-296)/(-162)) )

x-((-2*16558^(1/2)-296)/(-162)) = 0 // + (-2*16558^(1/2)-296)/(-162)

x = (-2*16558^(1/2)-296)/(-162)

( x-((2*16558^(1/2)-296)/(-162)) )

x-((2*16558^(1/2)-296)/(-162)) = 0 // + (2*16558^(1/2)-296)/(-162)

x = (2*16558^(1/2)-296)/(-162)

x in { (-2*16558^(1/2)-296)/(-162), (2*16558^(1/2)-296)/(-162) }

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