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

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Solution for (1/x-3)-(2/x+3)=1/(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:0) U (0:3) U (3:+oo)

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

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

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

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

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

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

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

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

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

14*x-7*x^2+3 = 0

14*x-7*x^2+3 = 0

14*x-7*x^2+3 = 0

DELTA = 14^2-(-7*3*4)

DELTA = 280

DELTA > 0

x = (280^(1/2)-14)/(-7*2) or x = (-280^(1/2)-14)/(-7*2)

x = (2*70^(1/2)-14)/(-14) or x = (-2*70^(1/2)-14)/(-14)

(x-((2*70^(1/2)-14)/(-14)))*(x-((-2*70^(1/2)-14)/(-14))) = 0

((x-((2*70^(1/2)-14)/(-14)))*(x-((-2*70^(1/2)-14)/(-14))))/(x*(x-3)) = 0

((x-((2*70^(1/2)-14)/(-14)))*(x-((-2*70^(1/2)-14)/(-14))))/(x*(x-3)) = 0 // * x*(x-3)

(x-((2*70^(1/2)-14)/(-14)))*(x-((-2*70^(1/2)-14)/(-14))) = 0

( x-((-2*70^(1/2)-14)/(-14)) )

x-((-2*70^(1/2)-14)/(-14)) = 0 // + (-2*70^(1/2)-14)/(-14)

x = (-2*70^(1/2)-14)/(-14)

( x-((2*70^(1/2)-14)/(-14)) )

x-((2*70^(1/2)-14)/(-14)) = 0 // + (2*70^(1/2)-14)/(-14)

x = (2*70^(1/2)-14)/(-14)

x in { (-2*70^(1/2)-14)/(-14), (2*70^(1/2)-14)/(-14) }

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