4/(x-9)+10/x=6

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Solution for 4/(x-9)+10/x=6 equation: 


D( x )

x = 0

x-9 = 0

x = 0

x = 0

x-9 = 0

x-9 = 0

x-9 = 0 // + 9

x = 9

x in (-oo:0) U (0:9) U (9:+oo)

4/(x-9)+10/x = 6 // - 6

4/(x-9)+10/x-6 = 0

(4*x)/(x*(x-9))+(10*(x-9))/(x*(x-9))+(-6*x*(x-9))/(x*(x-9)) = 0

10*(x-9)-6*x*(x-9)+4*x = 0

14*x-6*x^2+54*x-90 = 0

68*x-6*x^2-90 = 0

68*x-6*x^2-90 = 0

2*(34*x-3*x^2-45) = 0

34*x-3*x^2-45 = 0

DELTA = 34^2-(-45*(-3)*4)

DELTA = 616

DELTA > 0

x = (616^(1/2)-34)/(-3*2) or x = (-616^(1/2)-34)/(-3*2)

x = (2*154^(1/2)-34)/(-6) or x = (-2*154^(1/2)-34)/(-6)

2*(x-((2*154^(1/2)-34)/(-6)))*(x-((-2*154^(1/2)-34)/(-6))) = 0

(2*(x-((2*154^(1/2)-34)/(-6)))*(x-((-2*154^(1/2)-34)/(-6))))/(x*(x-9)) = 0

(2*(x-((2*154^(1/2)-34)/(-6)))*(x-((-2*154^(1/2)-34)/(-6))))/(x*(x-9)) = 0 // * x*(x-9)

2*(x-((2*154^(1/2)-34)/(-6)))*(x-((-2*154^(1/2)-34)/(-6))) = 0

( x-((-2*154^(1/2)-34)/(-6)) )

x-((-2*154^(1/2)-34)/(-6)) = 0 // + (-2*154^(1/2)-34)/(-6)

x = (-2*154^(1/2)-34)/(-6)

( x-((2*154^(1/2)-34)/(-6)) )

x-((2*154^(1/2)-34)/(-6)) = 0 // + (2*154^(1/2)-34)/(-6)

x = (2*154^(1/2)-34)/(-6)

x in { (-2*154^(1/2)-34)/(-6), (2*154^(1/2)-34)/(-6) }

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