(9/(x^2-4x))-(5/x)=(3/(x-4))

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Solution for (9/(x^2-4x))-(5/x)=(3/(x-4)) equation: 


D( x )

x = 0

x-4 = 0

x^2-(4*x) = 0

x = 0

x = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x^2-(4*x) = 0

x^2-(4*x) = 0

x^2-4*x = 0

x^2-4*x = 0

DELTA = (-4)^2-(0*1*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)+4)/(1*2) or x = (4-16^(1/2))/(1*2)

x = 4 or x = 0

x in (-oo:0) U (0:4) U (4:+oo)

9/(x^2-(4*x))-(5/x) = 3/(x-4) // - 3/(x-4)

9/(x^2-(4*x))-(3/(x-4))-(5/x) = 0

9/(x^2-4*x)-3*(x-4)^-1-5*x^-1 = 0

9/(x^2-4*x)-3/(x-4)-5/x = 0

x^2-4*x = 0

x^2-4*x = 0

x*(x-4) = 0

x-4 = 0 // + 4

x = 4

x*(x-4) = 0

9/(x*(x-4))-3/(x-4)-5/x = 0

9/(x*(x-4))+(-3*x)/(x*(x-4))+(-5*(x-4))/(x*(x-4)) = 0

9-5*(x-4)-3*x = 0

9-3*x-5*x+20 = 0

29-8*x = 0

(29-8*x)/(x*(x-4)) = 0

(29-8*x)/(x*(x-4)) = 0 // * x*(x-4)

29-8*x = 0

29-8*x = 0 // - 29

-8*x = -29 // : -8

x = -29/(-8)

x = 29/8

x = 29/8

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