x+1/x=12/(x-1)

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Solution for x+1/x=12/(x-1) equation:


D( x )

x = 0

x-1 = 0

x = 0

x = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

t_1 = 0

t_1-12*(x-1)^-1+x+x^-1 = 0

t_1-12/(x-1)+x+1/x = 0

(-12*x)/(x*(x-1))+(t_1*x*(x-1))/(x*(x-1))+(x^2*(x-1))/(x*(x-1))+(1*(x-1))/(x*(x-1)) = 0

t_1*x*(x-1)+x^2*(x-1)+1*(x-1)-12*x = 0

t_1*x^2-(t_1*x)+x^3-x^2-12*x+x-1 = 0

t_1*x^2-(t_1*x)+x^3-x^2-11*x-1 = 0

t_1*x^2-(t_1*x)+x^3-x^2-11*x-1 = 0

t_1*x^2-(t_1*x)+x^3-x^2-11*x-1

t_1*x*(x-1)+x^3-x^2-11*x-1

x^2*(x-1)+t_1*x*(x-1)-11*x-1

x^2*(x-1)-1*(11*x+1)+t_1*x*(x-1)

(t_1*x+x^2)*(x-1)-1*(11*x+1)

0*(t_1*x+x^2)

(0*(t_1*x+x^2))/(x*(x-1)) = 0

(0*(t_1*x+x^2))/(x*(x-1)) = 0 // * x*(x-1)

0*(t_1*x+x^2) = 0

t_1*x+x^2 = 0

x*(t_1+x) = 0

t_1+x = 0 // - t_1

x = -t_1

x*(t_1+x) = 0

0*x*(t_1+x) = 0

( t_1+x )

t_1+x = 0 // - t_1

x = -t_1

( x )

x = 0

x in { 0}

x belongs to the empty set

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