3-5/x-5=5/(x-2)(x-5)

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


D( x )

x-2 = 0

x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

x in (-oo:0) U (0:2) U (2:+oo)

3-(5/x)-5 = (5/(x-2))*(x-5) // - (5/(x-2))*(x-5)

3-((5/(x-2))*(x-5))-(5/x)-5 = 0

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

(-5*(x-5))/(x-2)-5/x-5+3 = 0

(-5*x*(x-5))/(x*(x-2))+(-5*(x-2))/(x*(x-2))+(-5*x*(x-2))/(x*(x-2))+(3*x*(x-2))/(x*(x-2)) = 0

3*x*(x-2)-5*x*(x-5)-5*(x-2)-5*x*(x-2) = 0

3*x^2-5*x^2-5*x^2+20*x+10*x-6*x+10 = 0

3*x^2-10*x^2+30*x-6*x+10 = 0

24*x-7*x^2+10 = 0

24*x-7*x^2+10 = 0

24*x-7*x^2+10 = 0

DELTA = 24^2-(-7*4*10)

DELTA = 856

DELTA > 0

x = (856^(1/2)-24)/(-7*2) or x = (-856^(1/2)-24)/(-7*2)

x = (2*214^(1/2)-24)/(-14) or x = (-2*214^(1/2)-24)/(-14)

(x-((2*214^(1/2)-24)/(-14)))*(x-((-2*214^(1/2)-24)/(-14))) = 0

((x-((2*214^(1/2)-24)/(-14)))*(x-((-2*214^(1/2)-24)/(-14))))/(x*(x-2)) = 0

((x-((2*214^(1/2)-24)/(-14)))*(x-((-2*214^(1/2)-24)/(-14))))/(x*(x-2)) = 0 // * x*(x-2)

(x-((2*214^(1/2)-24)/(-14)))*(x-((-2*214^(1/2)-24)/(-14))) = 0

( x-((-2*214^(1/2)-24)/(-14)) )

x-((-2*214^(1/2)-24)/(-14)) = 0 // + (-2*214^(1/2)-24)/(-14)

x = (-2*214^(1/2)-24)/(-14)

( x-((2*214^(1/2)-24)/(-14)) )

x-((2*214^(1/2)-24)/(-14)) = 0 // + (2*214^(1/2)-24)/(-14)

x = (2*214^(1/2)-24)/(-14)

x in { (-2*214^(1/2)-24)/(-14), (2*214^(1/2)-24)/(-14) }

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