(1/1-2)+(3/x+3)=(4/(x+3)(x-3))

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Solution for (1/1-2)+(3/x+3)=(4/(x+3)(x-3)) equation: 


D( x )

x = 0

x+3 = 0

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

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

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

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

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

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

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

x^2-4*x^2-2*x^2+3*x^2+15*x-6*x+3*x+9*x+9 = 0

x^2-6*x^2+3*x^2+9*x+3*x+9*x+9 = 0

3*x^2-5*x^2+12*x+9*x+9 = 0

21*x-2*x^2+9 = 0

21*x-2*x^2+9 = 0

21*x-2*x^2+9 = 0

DELTA = 21^2-(-2*4*9)

DELTA = 513

DELTA > 0

x = (513^(1/2)-21)/(-2*2) or x = (-513^(1/2)-21)/(-2*2)

x = (3*57^(1/2)-21)/(-4) or x = (-3*57^(1/2)-21)/(-4)

(x-((3*57^(1/2)-21)/(-4)))*(x-((-3*57^(1/2)-21)/(-4))) = 0

((x-((3*57^(1/2)-21)/(-4)))*(x-((-3*57^(1/2)-21)/(-4))))/(x*(x+3)) = 0

((x-((3*57^(1/2)-21)/(-4)))*(x-((-3*57^(1/2)-21)/(-4))))/(x*(x+3)) = 0 // * x*(x+3)

(x-((3*57^(1/2)-21)/(-4)))*(x-((-3*57^(1/2)-21)/(-4))) = 0

( x-((-3*57^(1/2)-21)/(-4)) )

x-((-3*57^(1/2)-21)/(-4)) = 0 // + (-3*57^(1/2)-21)/(-4)

x = (-3*57^(1/2)-21)/(-4)

( x-((3*57^(1/2)-21)/(-4)) )

x-((3*57^(1/2)-21)/(-4)) = 0 // + (3*57^(1/2)-21)/(-4)

x = (3*57^(1/2)-21)/(-4)

x in { (-3*57^(1/2)-21)/(-4), (3*57^(1/2)-21)/(-4) }

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