(1/x)+(1/(x+11))=(21/(11x+33))

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Solution for (1/x)+(1/(x+11))=(21/(11x+33)) equation:


D( x )

x+11 = 0

x = 0

11*x+33 = 0

x+11 = 0

x+11 = 0

x+11 = 0 // - 11

x = -11

x = 0

x = 0

11*x+33 = 0

11*x+33 = 0

11*x+33 = 0 // - 33

11*x = -33 // : 11

x = -33/11

x = -3

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

1/(x+11)+1/x = 21/(11*x+33) // - 21/(11*x+33)

1/(x+11)-(21/(11*x+33))+1/x = 0

1/(x+11)-21*(11*x+33)^-1+1/x = 0

1/(x+11)-21/(11*x+33)+1/x = 0

(1*x*(11*x+33))/(x*(x+11)*(11*x+33))+(-21*x*(x+11))/(x*(x+11)*(11*x+33))+(1*(x+11)*(11*x+33))/(x*(x+11)*(11*x+33)) = 0

1*x*(11*x+33)-21*x*(x+11)+1*(x+11)*(11*x+33) = 0

11*x^2-10*x^2-198*x+154*x+363 = 0

x^2-44*x+363 = 0

x^2-44*x+363 = 0

x^2-44*x+363 = 0

DELTA = (-44)^2-(1*4*363)

DELTA = 484

DELTA > 0

x = (484^(1/2)+44)/(1*2) or x = (44-484^(1/2))/(1*2)

x = 33 or x = 11

(x-11)*(x-33) = 0

((x-11)*(x-33))/(x*(x+11)*(11*x+33)) = 0

((x-11)*(x-33))/(x*(x+11)*(11*x+33)) = 0 // * x*(x+11)*(11*x+33)

(x-11)*(x-33) = 0

( x-11 )

x-11 = 0 // + 11

x = 11

( x-33 )

x-33 = 0 // + 33

x = 33

x in { 11, 33 }

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