(2/x-5)-(2/x)=10/(x^2-5x)

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Solution for (2/x-5)-(2/x)=10/(x^2-5x) equation: 


D( x )

x = 0

x^2-(5*x) = 0

x = 0

x = 0

x^2-(5*x) = 0

x^2-(5*x) = 0

x^2-5*x = 0

x^2-5*x = 0

DELTA = (-5)^2-(0*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+5)/(1*2) or x = (5-25^(1/2))/(1*2)

x = 5 or x = 0

x in (-oo:0) U (0:5) U (5:+oo)

2/x-(2/x)-5 = 10/(x^2-(5*x)) // - 10/(x^2-(5*x))

2/x-(10/(x^2-(5*x)))-(2/x)-5 = 0

2/x-10*(x^2-5*x)^-1-2*x^-1-5 = 0

2/x-10/(x^2-5*x)-2/x-5 = 0

x^2-5*x = 0

x^2-5*x = 0

x*(x-5) = 0

x-5 = 0 // + 5

x = 5

x*(x-5) = 0

2/x-10/(x*(x-5))-2/x-5 = 0

(2*(x-5))/(x*(x-5))-10/(x*(x-5))+(-2*(x-5))/(x*(x-5))+(-5*x*(x-5))/(x*(x-5)) = 0

2*(x-5)-2*(x-5)-5*x*(x-5)-10 = 0

2*x-5*x^2-2*x+25*x-20+10 = 0

25*x-5*x^2-10 = 0

25*x-5*x^2-10 = 0

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

5*x-x^2-2 = 0

DELTA = 5^2-(-2*(-1)*4)

DELTA = 17

DELTA > 0

x = (17^(1/2)-5)/(-1*2) or x = (-17^(1/2)-5)/(-1*2)

x = (17^(1/2)-5)/(-2) or x = (17^(1/2)+5)/2

5*(x-((17^(1/2)-5)/(-2)))*(x-((17^(1/2)+5)/2)) = 0

(5*(x-((17^(1/2)-5)/(-2)))*(x-((17^(1/2)+5)/2)))/(x*(x-5)) = 0

(5*(x-((17^(1/2)-5)/(-2)))*(x-((17^(1/2)+5)/2)))/(x*(x-5)) = 0 // * x*(x-5)

5*(x-((17^(1/2)-5)/(-2)))*(x-((17^(1/2)+5)/2)) = 0

( x-((17^(1/2)+5)/2) )

x-((17^(1/2)+5)/2) = 0 // + (17^(1/2)+5)/2

x = (17^(1/2)+5)/2

( x-((17^(1/2)-5)/(-2)) )

x-((17^(1/2)-5)/(-2)) = 0 // + (17^(1/2)-5)/(-2)

x = (17^(1/2)-5)/(-2)

x in { (17^(1/2)+5)/2, (17^(1/2)-5)/(-2) }

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